Ephesians 2:1 and Colossians 2:13 state that people are dead in sin until they are born again.(/QUOTE]
Eph 2:1 And you
He made alive, who were dead in trespasses and sins,
Eph 2:2 in which you once walked according to the course of this world, according to the prince of the power of the air, the spirit who now works in the sons of disobedience,
Eph 2:3 among whom also
we all once conducted ourselves in the lusts of our flesh, fulfilling the desires of the flesh and of the mind, and were by nature children of wrath, just as the others.
By the language highlighted above, Paul seems here to be referring to sins committed by his audience, not sins inherited from forebears at conception or birth.
We do not die as a result of committing a sin. We die because death is lodged in us as a result of Adam's disobedience, 1 Corinthians 15:22.
1Co 15:21 For since by man
came death, by Man also
came the resurrection of the dead.
1Co 15:22 For as
in Adam all are dying, (ἐν τῷ Ἀδὰμ πάντες ἀποθνῄσκουσιν, present active indicative) even so
in Christ all shall be made alive (ἐν τῷ Χριστῷ πάντες ζῳοποιηθήσονται, future passive indicative).
1Co 15:23 But each one in his own order: Christ the firstfruits, afterward those
who are Christ’s at His coming.
1Co 15:24 Then
comes the end, when He delivers the kingdom to God the Father, when He puts an end to all rule and all authority and power.
All were in Adam genetically when Adam walked the earth. Any descendant of Adam was in Adam, and may be described as being "in Adam". Likewise, all those imparted with Jesus' Spirit to become born again are "in Christ" and will be resurrected in a physical body alike in nature to His own physical body. This text does not say all are born sinful.
Adam's death was not physical. He lived nearly 1,000 years. But it is obvious that there was a separation between God and Adam after Adam disobeyed. God did not reject Adam. Adam hid from God. And this is true of all mankind. You do not have to teach a child to rebel. It's in its nature.
Gen 2:17
“but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die. (מוֹת תָּמוּת infinitive absolute + qal imperfect)”
Adam was told "In the day you eat of it, to die you shall be dying." This expression does not indicate
immediate death, but a gradually dying leading to death. The same grammatical structure is used in other places in scripture and is translated as "shall surely X" where it obviously does not mean an immediate outcome, but the beginning of a gradual outcome. So, Adam was told that In the day you eat of it you will begin dying and will eventually die." We could say it idiomatically as " In the day you eat of it, your days will be numbered."
Compare
Gen 18:18 “since Abraham
shall surely become (הָיוֹ יִהְיֶה To become he shall be becoming, Infinitive absolute + qal imperfect) a great and mighty nation, and all the nations of the earth shall be blessed in him?
Romans 2 states how those without the law still sin and come under God's judgement. No one is born knowing the law. All are born dead in trespass and sin.
Rom 2:12 For as many as
(ἥμαρτον ἀνόμως) will also perish without law, and as many as
sinned in the law (ἐν νόμῳ ἥμαρτον) will be judged by the law
Rom 2:25 For circumcision is indeed profitable if you keep the law; but if you are
a breaker of the law (παραβάτην νόμου), your circumcision has become uncircumcision.
Rom 2:27 And will not the physically uncircumcised, if he fulfills the law, judge you who,
even with
your written
code and circumcision,
are a transgressor of the law (παραβάτην νόμου)?
Those without the Mosaic law sin by falling short (hamartanO) of the glory God made it possible for us to walk in. Those with the Mosaic Law sin by transgressing (parapiptO) that Law.
So yes, those without the law still sin in the hamartanO sense, but not in the parapiptO sense, according to Adam's sin.
I do not believe that those who die in infancy are rejected by God. There is an age of responsibility when people know the difference between good and evil. Up until then, God accepts the innocent because of the sacrifice of Jesus.
God does not reckon hamartia, falling short of His glory, to us. So, the child is innocent, until they start breaking laws they know are from God. God accounts our transgressions (paraptOma)