What Does It Mean That God Desires All People To Be Saved?

I can go along with that, and there's scripture to suggests just that in the parable of the prodigal. While the son was afar off (on his way back to his father) his father ran to meet and embraced him.

Right, the god of this world blinded the minds of unbelievers, lest (which meaning translates as 'perhaps no' or something like, 'hoping not')
the light of the glorious gospel of Christ, who is the image of God, should shine unto them.
It wasn't God that blinded them as in the case with Israel or Saul, for his respective purposes.

But if our gospel be hid, it is hid to them that are unbelievers, by the god of this world.
Let's back up to 2Cor chapter 3 comparing the glory of the old covenant against the new

14But their minds were closed. For to this day the same veil remains at the reading of the old covenant. It has not been lifted, because only in Christ can it be removed. 15And even to this day when Moses is read, a veil covers their hearts. 16But whenever anyone turns to the Lord, the veil is taken away.

anyone means anyone.

Nobody said that salvation is by any other method but grace.. The huge error that you have come to is to believe that Faith is a works when the Bible clearly makes a distinction between works and faith by saying that salvation is by Faith not works.. If Faith was a works then the bible would never say that.. So Faith can never be a works..

Of course the Holy Spirit convicts us human beings and then if we respond with meekness and acknowledge our sin and our need for salvation then we embrace the Atonement of the LORD Jesus.. I don't believe that an unrepentant sinner is saved..

And the Bible declares that people can and have resisted the call of the Holy Spirit..

(Acts 7:51-53) "¶ Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost: as your fathers did, so do ye. {52} Which of the prophets have not your fathers persecuted? and they have slain them which shewed before of the coming of the Just One; of whom ye have been now the betrayers and murderers: {53} Who have received the law by the disposition of angels, and have not kept it."

Now in the calvinist doctrines ""Irresistible grace"" no one can resist the moving of the Holy Spirit.. Of course calvinism is a false interpretation of scripture..

It does say that belief is a work. The below verse clearly tells us that belief is both a work and that it is God's work alone
to accomplish within us. Anything that someone of themselves must to for salvation regardless of what it may be
makes it a work. If it is a requirement for salvation, then it is not only a work but also a law. But the Bible
clearly informs that no man can be saved by trying to achieve the works of law. Grace requires nothing but itself -
it is all encompassing.

[Jhn 6:29 KJV] 29 Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent.

Belief is not a Works..

(Romans 4:1-5) "What shall we say then that Abraham our father, as pertaining to the flesh, hath found? {2} For if Abraham were justified by works, he hath whereof to glory; but not before God. {3} For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness. {4} Now to him that worketh is the reward not reckoned of grace, but of debt. {5} But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness."

So the above scripture makes it clear that Belief is not a Work.. Because him that worketh not But believes on Jesus is justified.. If Belief was a works then this verse would make no sense..

(Romans 3:27-28) "Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith. {28} Therefore we conclude that a man is justified by faith without the deeds of the law."

Again if Faith was a Work then the above would make no sense because it clearly makes a distiction declaring Faith to not be a Works..

Yes, but it means spiritually blinded, not physically blinded.

No, it doesn't. How can someone turn to Christ if they are spiritually dead and blind and therefore oblivious to the true Christ? To do so, they must first be given spiritual life and through spiritual life, spiritual sight, but that comes only from being saved/born-again. To see spiritually and to turn to Christ are only given to the elect - they are byproducts of salvation but themselves do not cause salvation, nor is it a choice that unsaved man can make- they come only as gifts from God - but only to some.
Notice the "blessed" below. It is saying that for one to see spiritually, their eyes must first have been blessed by God, meaning blessed from/by becoming saved/born-again.

[Mat 13:16 KJV] 16 But blessed [are] your eyes, for they see: and your ears, for they hear.

For someone to truly comprehend Christ and salvation, their sins must first be forgiven by God and given spiritual life.

[Luk 1:77 KJV] 77 To give knowledge of salvation unto his people by the remission of their sins,

No one can truly believe unless and until first becoming saved, by which, they are indwelt with/by the Holy Spirit and become born-again. The Holy Spirit imputes Christ's faith unto them and from that imputation of faith, they come to a true belief in Christ.

[Gal 5:22 KJV] 22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith,

What Does It Mean That God Desires All People To Be Saved?
Our Father loves us. He wants us with Him in the ETERNITY, which is after this life, after the Millennium and after the Great White Throne Judgment.

It is a work and I guess you decided to ignore the verse I provided that says it is a work. The "his faith" above is Christ's faith, not their faith. A person's faith has no righteousness, only Christ's faith does. See the following verse.

[Phl 3:9 KJV] 9 And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:

The "counted to him for righteousness" is that Abraham accounted his belief to God - that God is righteous.
Notice in the below, that we are clearly told God's righteousness is made manifest (revealed) by it being given from "faith to faith; that is, it originates as Christ's faith and is imputed to those whom God has chosen to save.

[Rom 1:16-17 KJV]
16 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.
17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.

It does make sense, but you attribute faith to the wrong person/source. The law of faith is speaking of justification by Christ's faith, not a person's faith. Again, if someone has to have faith to be saved, that requirement makes the having of faith into a law besides that it is a work. But man cannot be saved by their works of law, only by Christ, so it cannot be speaking of a faith which supposedly originates from a man.

[Gal 2:16 KJV] 16 Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.

He doesn't desire all people to be saved - if He did, they would become so. Did you notice the "my sheep hear my voice" part of the verse you quoted? It means that if someone is not of His sheep, they will not be able to hear His voice; if they cannot hear His voice, then they also can't know Christ; if they can't know Christ, then God does not desire all to be saved, but only those whom He allows to hear His voice. So, they must first be of His sheep to hear, and therefore, because they cannot hear, they are not His sheep. Man cannot give to
himself spiritual hearing - it comes only as a gift from God.

For this is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth. For there is one God and one Mediator between God and men, the Man Christ Jesus, who gave Himself a ransom for all, to be testified in due time,

- 1 Timothy 2:3-6

Not everyone is Elect. Some folks have Free Will. This is why the Gospel is preached.

Yes, but you have to look further to let the Bible define who the "all" represents. The "all" are they whom God had chosen to salvation and gives to the Son, but that is not everyone ever born. Since all do not become saved, then it must be that it was not the Father's intention that all become saved, because not all are given to the Son by the Father for salvation - otherwise, He would have given all to the Son, and those whom He gives they MUST become saved: none of those given to the Son by the Father can be lost, and they and they alone, must be raised on the last day. Notice in the below verses that no provision is included for man contribute anything to his salvation - it is a proposition exclusively between the Father and Son, not man.
Observe:

[Jhn 6:37, 39 KJV]
37 All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out. ...
39 And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day.

No. The gospel is preached to edify and teach the elect/saved on the doctrines of Christ and of salvation. If someone is not
saved, they cannot hear spiritually and so preaching will have no effect upon them no matter how many times it is repeated to them.

[Eph 4:11-13 KJV]
11 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;
12 For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ:
13 Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ:

No, we disagree.

Okay.

You are speaking of knowing Christ here, and they come to know through the Spirit that witnesses in their hearts that they are children of God, and faith is not equivalent to knowing.

The Holy Spirit is only given to those who become saved and not until then - the Holy Spirit and faith come to someone from salvation, as the fruit of the Spirit. If they are the children of God as you say, then they already have become saved - that being the only way to be a child of God (see Luke 20:36 below)? According to your belief (as I understand it), is it is up to a person to produce their own saving faith and not receive it solely as a gift from God- that being what you consider free-will. If that is what you think, then how does someone give to themselves saving faith without first having a true knowledge of salvation upon which that faith would have to be built, which knowledge, according to Luke 1:77, can only come from salvation, and not before salvation? IOW, how can someone believe in something that they don't know, yet, they can only know it by their sins being forgiven, meaning that they had first become saved, as per Luke 1:77 (notice the "by" in that verse)?

[Luk 20:36 KJV] 36 Neither can they die any more: for they are equal unto the angels; and are the children of God, being the children of the resurrection.

[Luk 1:77 KJV] 77 To give knowledge of salvation unto his people by the remission of their sins,

as Job said, my ears have heard of you but now my eyes see you. Job had faith, ears hearing, before he knew, eyes seeing.

He already was saved, by which, he was given the Holy Spirit.