I drew this endgame - Black to move what could I do to pass the pawn and win?

I played the pawn btw but that let to a draw. Now what's the sequence to win this? Or is that not possible unless he blunders? Feels like it would be a back and forth until it's a draw, even if I move the king to the 4th rank to give him room.

What @Fet says is true, but I interpreted that you had the pawn on g4 @Hightider (and pushed it to g3 when you essentially gave up at making progress). If your pawn was back on g4 and the enemy king had "King Opposition" then it's a draw still. If not, then you can win.

Edit: It's been pointed out to me that my above statement with the pawn on g4 is a win regardless who to move (I forgot about the g-pawn push to g3 passing the tempo back to the opponent). The rest I shared about King Opposition and the winning technique is still correct though and the position with the pawn on g3 is indeed drawn with best defense.

I highly recommend checking out this chess video I made on the winning technique for this pawn endgame:

This is the position on move 56.Kxg3 and it is now Black to move. Right here it is a drawn game unless white misplays. In order to promote, you must get your K in front of your pawn which you can't do. 56. ..Kh6 is met with 57. Kg4 or Kh4 stopping your K from advancing. It also does no good playing 56. ...Kg7 because white can play 57. Kf4 or Kg4 or Kh4 which all lead to prevention of your King advancing. Understanding of a drawn position comes from earlier than the position you showed.