Does the sovereignty of God nullify the grace of God?

If we go solely by the Bible, God's sovereignty went out to the entire world in John 3:16. Even Romans one tells us everyone knows about God and that God has made Himself known to all which makes everyone who lived accountable for their salvation status. It's seems rather clear the "Elect" are merely those who chose to accept God's invitation.

I believe that we have had this conversation before, but I don't mind refreshing your memory.

Jesus did not die for all mankind's sins, only the elect of whom God gave him (John 6 :39) Those that he redeemed were from every kindred, and tongue, and people, and nation.(Rev 5:9-10).

God's elect are of the household of Jacob/Israel, which is spiritual Israel, ant there is the remnant of Jacob/Israel (Zeph 3:11-13). Jacob/Israel were disobedient to God and he blinded their eye's to understand the doctrine of Christ, and revealed it to the remnant of Jacob/Israel.

Disobedient Jacob/Israel is referred to, in the scriptures, as the lost sheep of the household of Jacob/Israel. These are who God instructed the remnant to preach to. Not to save (deliver) them eternally, but to save (deliver) them from their ignorance of the doctrine of Christ.

The book of Romans was written by Paul, and directed to the church in Rome who are the called of Jesus Christ (Rom 1:5-7). There is a deliverance (salvation) when a babe in Christ comes unto a knowledge of the truth of Christ's doctrine.

Heb 5:12~~

For though by this time you ought to be teachers, you have need again for someone to teach you the elementary principles of the actual words of God, and you have come to need milk and not solid food.

Same words can be interpreted by Greek differently in the scriptures, such as the word die is interpreted as meaning "a separation" The first death is when the elect die to sin in their new spiritual birth. When they pass from this life, their souls goes back to God and he considers them as asleep in the grave.

Those souls who are not God's die their first death, along with their souls, when they pass from this life, and their second death is at the Judgement. God's elect are judged as they live here on earth by God's chastening, and are not judged at the last day.

This scripture inin reference to those who have been born again.

What must I do to be saved?

I respect your dedication to the word of God.

Whom the Lord loveth, he chastens, and scourgest every son whom he receveth

God does not chasten those that are not his elect (Psalms 73) nor judge them until the last day judgement.

What is God's will/desire for the non elect?

So? That does not mean their soul does not belong to God. Think about it.
If they did not belong to Him, what right has He to decide their forever fate?
Plus, He judges ALL.

And thank you...

If you are referring to eternally, nothing.

If you are referring to a timely deliverance (salvation) there are many things we must do.

If you are referring to the Jews that Peter was accusing of crucifying Christ, they were already born again, because they have had their heart of stone replaced with a fleshy heart that can be "pricked" to feel spiritual guilt. Notice their response.

If you want to see the response of a heart of stone read Acts 7:54, and notice their response, when they heard Stephen preach the same sermon as the born again Jews heard Peter preach.

None, he leaves them to their own destruction, read Psalms 73.

God does not decide their fate, he leaves them to their own destruction. If he decided their fate, he would be an unjust God. Why God did not choose all humanity to be saved (delivered) eternally, I know not. Who am I to ask God, What doest thou? (Dan 4:35)

Kroogz said:
What must I do to be saved?
~~~~~~
Acts 16:31 “And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.”

So, if you have kids, a wife, mother and dad and they just happen not to be "elect"(as you perceive elect to mean), you're ok with that?
Does God love your parents, wife and kids like you do?
Does God love your enemies? (the ones who are lost non-elect sinners)
If God does not love your lost enemies then He requires you to do something He can't or won't.

Matthew 5:44 But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;...............................45That ye may be the children of your Father which is in heaven:...............

Basically, what it's saying, is "to be like God is, love your enemies". So, if God doesn't really love all those lost people who aren't going to Heaven, then He just lied. And we know that ain't so.

What do you believe the most loving thing God can do?

It's the milk of His word. If a believer cannot answer that simple question......
Heb 5:12~~

For though by this time you ought to be teachers, you have need again for someone to teach you the elementary principles of the actual words of God, and you have come to need milk and not solid food.

The Lord Jesus Christ paid for the sins of the WHOLE world. John 3:16. He propitiated His Father by His life, death And resurrection on the Cross. He reconciled the WHOLE world to Himself. He tore the veil( ALL can come to Him.) Acts 16:31. Equal privilege, equal opportunity.

ALL sin is judged and nailed to the Cross. What we have left is believe or not. Those who believe.....Eternal life. Those who don't believe....Lake of Fire, According to their DEEDS(All sin is judged.)

Rev 20:12~~And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.

Matt 7~~22 Many will say to Me in that day, ‘Lord, Lord, have we not prophesied in Your name, cast out demons in Your name, and done many wonders in Your name?’ 23 And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness!’

Psalm 9~~7 The LORD reigns forever; he has established his throne for judgment.
8 He rules the world in righteousness and judges the peoples with equity.

God never intended one man to end up in hell. Hell was not prepared for man.

Matthew 25:41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:

And as Magenta explained, man is appointed once to die. No man is appointed to die twice. That was not part of God's plan.

How did you miss John 3:17, and the verse before that (and all similar verses)? For God sent not his Son into the world to condemn the world; but that the world through him might be saved.