Found by Patafoin on Discord, who did this on Titanic Monarch 1

I'm guessing it's a frame-perfect trick, since I just tried a run and didn't manage it.

If you check the video description Claris explains that there's a 2 frame window about 10-12 frames after the end of the score screen that you have to hit to get it.

Confirmed also possible on PC:

Can you mash the pause button, or does it have to be a carefully timed press?

It's MUCH better to not mash, the menu lets you close it really quick so you're likely going to just instantly close it if you mash.

I had gotten this in practice but I didnt see this video when I got it so I thought it would be faster to exit and select the next level rather than restart. Now is it specific to the cut-scenes shown or can it be done for any?

Bump.

In Sonic Mania Plus, you can now just mash the button in order to skip the cutscene. I tried this with Encore Green Hill, Encore Chemical Plant, and Regular Green Hill with Mighty.

You don't even have to mash. Just press the start button once the cutscene has started and it will move to the next level. 2 frame cutscene skips are no longer a thing. The only stage this doesn't seem to work for is Hydrocity 2.

Do you know if you can skip the intro cutscene in mania plus?

@Newton yes you can.