If Titanic hadn’t been released in 1997, who would have won?

I think that Good Will Hunting probably would have won because it had Harvey, and the narrative of the two hot new stars in Matt and Ben.

I guess it could have been L.A. Confidential since that had the critics backing, but at least from what I remember, it didn't really have a narrative other than being the critics favorite. Maybe that would have been enough since it did win all top 3 critics' groups plus NBR, but I still think voters wouldn't be able to resist Harvey's razzle dazzle at that time. Good Will Hunting had the feel good story plus two hot stars that wrote the screenplay themselves, and I can only imagine the hit pieces Weinstein would have done to L.A. Confidential. "Why should a second rate Chinatown win Best Picture?" "Russell Crowe will never be as famous as Matt Damon." Stuff like that behind the scenes.

As for what would have taken Titanic's place in Best Picture, I know Atom Egoyan got a Best Director nomination, but I think Boogie Nights would have got in based on having more support from actors, and The Sweet Hereafter probably not having enough support overall to get in. Although maybe Amistad would have done better if Titanic hadn't been in the race, or maybe Miramax would have thrown more support behind Jackie Brown too if there was no Titanic.

It definitely wouldn't be Full Monty, but otherwise a tough call...

Good Will Hunting has Screenplay and Supporting Actor.
As Good As It Gets had Actor AND Actress-- don't underestimate it
LA Confidential had Screenplay and Supporting Actress.

On paper, three very strong contenders. I'll throw Boogie Nights in for consideration to, imagining an alternate reality it scooped up lots of extra nominations in Titanic's stead.

Best Director-- Curtis Hanson would be runner-up, but its the 90s so they wouldn't split if they gave BP to something else. Brooks doesn't have a nomination here, but either he or Anderson would be sans Cameron.

Best Leads-- As Good As It Gets sweeps it up. Good Will Hunting has Matt Damon, but no comparison.

Supporting-- Robin Williams is a bigger win than Kim Basinger. It also has Minnie Driver going for it. As Good As It Gets has Kinnear, but Boogie Nights probably has the best ensemble.

Screenplay-- Good Will Hunting is a bigger win than LA Confidential to me (and to pop culture). As Good As It Gets (and Boogie Nights again) are very strong nominees though.

Editing-- LA Confidential was most likely to be runner up, but Good Will Hunting and As Good As It Gets all nominated. Boogie Nights could have been.

Techs-- LA Confidential is the biggest tech player by far: nominations for Sound, Art Direction, Cinematography.

That gives LA Confidential everything tech-based, but that doesn't always mean everything.

I think they'd give Picture and Director to Good Will Hunting.

I don't know The Full Monty was probably in the race to some degree since it won SAG ensemble, but granted that meant less then.

It probably was Good Will Hunting, based largely on the "Weinstein effect", which fully took hold the following year.

I'm inclined to think Good Will Hunting wins Best Picture, Hanson wins Best Director.

I thought about that because it did end up winning BAFTA too, but I still don't think it would have had enough support to win Best Picture with both Good Will Hunting and L.A. Confidential being American productions, and L.A. Confidential possibly getting traction for as  mikediastavrone96 mentioned for shooting in L.A. and having the L.A. connection. Then of course GWH would still have the same narrative of two young stars writing their own film and becoming successes. 

Plus you're right back then SAG was even more wonky than it has been in the past couple of years, minus this year where it did show how strong Parasite was, and The Birdcage had just won the year before, so while I think it did show there was support and love for The Full Monty, it wouldn't necessarily translate to Best Picture.

It would have had the same underdog narrative so that would have been the same, but I think without a big film like Titanic, it might not even have been as effective because I know one of the stories that year was how The Full Monty managed to make so much money as opposed to something like Titanic which obviously made tons of money too, but also cost so much money to make that many were worried it was going to bomb. 

Fox Searchlight wasn't the awards powerhouse that they are today, so that makes a big difference too. Or if Harvey was the one behind The Full Monty, I could believe that he'd convince enough voters somehow that it should win, so in the end I think it winds up with the same nominations and same wins. 

The Full Monty nomination feels like the obligatory across the pond nomination that the academy seemed to love rewarding every year back in the day (think Four Weddings, and The Ivory / Merchant films). It never stood a chance of winning, if anything its reward was its nomination (it certainly helped its box office in NA too, although it didn't do too bad before the big nomination). It also had a huge effect, being the film that basically broke Fox Searchlight into the echelon of highest award consideration ranking. 

The interesting thing about precursors in general, is that SAG and other award circuits back then felt like they were sometimes less concerned with awarding with what they think would win (although they still do that, now and again), but instead going for random out of left field choices like The Birdcage winning or Get Shorty getting a nomination the prior year. I really miss when award shows like that were more creative.