Will he have to pay?

My ex and I have been broken up since I found out he was cheating on me multiple times with different girls during my pregnancy. He never paid for one single thing for this baby. Didn’t want to go to appointments and was just unsupportive and would say horrible things to me and made my pregnancy not as special as I had hoped it would be,

He has not paid for anything during this pregnancy and since she’s been born (she’s 6 weeks old) he hasn’t actually bought anything for her. Yet he is pushing to be at my house all the time to see her and me (because he wants me to get back with him and for him to move in with me... but that’s never happening!!). So he is wanting the role as dad but with no responsibility.

If I was to apply for child support (I have not yet), would he have to pay for the previous 6 weeks that he didn’t support us for?

(He always says he’s going to pay for things but he ends up gambling and spending it on drinks and other random items instead)