The obvious answer for a question like this is often a movie with some kind of big twist - which does make a recommendation pretty hard if you want to preserve the surprise of the twist.

In an alternate vein, I think horror movies have a lot of potential here. I used to have a subscription to Shudder, and watching old horror movies I had never seen was a special kind of experience. Ditto for anything that describes itself as a "mind-bending psychological thriller" or anything psychedelic

For a specific recommendation, I'm going with Blood Beat (1983). Although even if I didn't go in blind I probably would have found it just as weird