The Question of the ages

Hi! I’ve been catholic my whole life, and one thing that nobody can explain is this:

Jesus died on the cross for our sins, he died and took the sins of man with him, but when we are born, we are born with sin, so if he died so we could not have sin how’s it possible we were born with it? I’ve read the Bible (it’s been years) and I feel like I’m missing something.