That's a very good question. From the teasers we already know the show will at least get to winter. Though from the looks of it, it seems they will deviate from what happens during that part of the game (which makes sense, tbh). That only leaves the last section of the first game to cover, so they would have to create some sort of new plot to leave as a season ending cliffhanger if they want to do the 1st game's ending in Season 2.
I remember reading somewhere that Pedro Pascal said that season 1 is too short. I don't know if he was just being hyperbolic because it's so good or what.
Would be a letdown(and rushed) if they literally get to the end of the story in part 1 by the end of the season. Do we even know how many episodes season 1 has yet?
If they're going to make this into a multi-season big thing, they're going to need to build a lot of history and love for all the characters that way when Abby and the rest to get introduced it hits that much harder. But then again they killed off Ned Stark in season 1 of Game of Thrones and that hit. So who knows.
Edit:
Just did a quick Google search and apparently season one will have 10 episodes. So roughly 10+ hours of content.
Definitely a lot of time there to get to the end possibly. For perspective from beginning to end Last of Us part 1 cutscenes equals out to about 5 hours. I would prefer if they stretch it out to at least two seasons though for part one.