Well they sinned by and through their representative and so they are born as ungodly sinners worthy of hell
No, they did not commit any sin, they inherited a sin nature from their parents going all the way back to Adam. Everyone is to be evaluated/judged on their works. A baby has no works to be judged.
For believers:
2 Corinthians 5:10
For we must all appear before the judgment seat of Christ, that each one may receive
the things done in the body, according to what he has done, whether good or bad.
For unbelievers:
Revelation 20:12
And I saw the dead, small and great, standing before God, and books were opened. And another book was opened, which is
the Book of Life. And the dead were
judged according to their works, by the things which were written in the books.
People are now condemned on the basis of their response to Christ, not on their sin. Sin has been dealt with, Christ died for the sin of the world, it is finished.
John 3:18
“He who believes in Him is not condemned; but he who does not believe
is condemned already, because he has not believed in the name of the only begotten Son of God.