I do use Youtube. Through newpipe though. I'll extend your premise , and presume there is no large tech company holding any site or service online. That also includes any generative AI.

How would I use internet?

Well, the same I did in the early 90s I guess. I can't fathom it would be long before some kind of search engine popped up though. I guess I'll be searching art online and sharing mine on platforms similar to Deviantart or the likes, if DA doesn't exist I one hundred percent believe there would be online forums dedicated to sharing art and connecting through messages. I would probably also be text roleplaying in forums as well. Those things still exist on a small scale today.

I guess I would also connect to check news to a couple official news sites if there is no such thing as rss. Same for weather forecast.

I wonder what the situation would be about maps. Without Google, would we still have something large and accessible such as OSMand? I believe not only we would, they would be better, and they would probably be easier to use downloaded locally so that's probably another thing I'd do.

Do we still have torrenting? I can see myself torrenting even more if I don't have any streaming platforms.