Bit of a weird choice but maybe Dick Figures The Movie. It was based off of an animated YouTube series and if I recall correctly they got it out near the height of their relevance. It’s not like the Angry Birds movie where it acted as more of a reminder that it was a thing than anything else.

Technically not debut, but Sam Raimi’s Spider-Man was well timed.

It was shortly after the run of the 90s TV cartoon. VFX had just reached a point where convincing web slinging could be made. A few years earlier it would’ve looked awful.

I would also say that along with X-Men it started a new era of super hero movies where they could be taken seriously. Compare it to the Batman movies in the 90s, which are goofy in comparison.