I went in with mid-level expectations, which probably helped. However there were a bunch of things that helped me warm up to the movie.
First is that, with one exception, it sticks mostly to stuff from the earliest games, anything from later is just a cheeky little reference. For me, FNAF will always be the original five plus Springtrap, none of the Remnant bullshit from the games was here, it was more straight paranormal.
One recurring thing that made me warm up was this avoided a lot of common traps in horror movies.
First, the protagonists are all very quick to catch on to things, almost as quick as the audience. When Vanessa knew where the restaurant keeps the tablecloths, I expected this to be one of those things that is a hint for the audience but that the main character never latches onto, but nope... within seconds he's outright saying "Wow you have a suspicious amount of knowledge."
Another thing Horror movies do that I usually dislike, is introducing a "monster" that is actually totally capable of speech and reason, but then still having them be someone you can't reason with or behave in totally nonunderstandible ways. This movie?... does the opposite. You quickly realize the animatronics are just kids, and they want to hang out with the little girl, and there's actually some warm moments where even the adults seem like they're bonding with them. Frankly if the danger element hadn't been introduced later, I could imagine Mike Shmidt actually liking this particular night job.
Which, even that danger element... the resolution involves communicating with the animatronics and letting them in on what really happened/who their enemy is, not them just being mindless servants of the bad guy.
Which even that makes some sense. I'm guessing from their dream interactions that this sort of implies a limited amount of cognition on the dead kids' part, and we all know how in dreams, we think weird. I could see them maybe misremembering the golden rabbit as a friend up until Abby's picture reveals the truth to them.
I think the real real I connected with it is that, instead of being straight "horror movie," its more like horror-fantasy in the vein of something like the old Goosebumps TV show--which makes sense as FNAF itself has become basically Goosebumps for modern kids (though Goosebumps had more range). As such, it actually avoided a lot of the cringe trappings of the horror genre.
And as a FNAF movie, its just nice that the movie tells a story and isn't just autistic theory-bait, which is what I went in expecting.