If the Elf can give themselves infinite life in response to the infinite damage, then they have essentially won, because however much damage the Goblin would deal, they can just go "OK, but before that damage applies I give myself enough life to survive". The Goblin deck can never reach a game state where they win.

If the combos are sequential and the Elf has to commit to a certain number of life before the Goblin commits to a certain number of damage, then the Goblin would win.

There are some other possible intricacies (can they give themselves 1 life infinite times? or infinite life once?) From the mechanics of how the game usually goes, I would assume the first case applies here.