I would suggest creating a short list of broad “top-level categories” that every other category can be grouped into (maybe around 20 of them). For example:
Technology, Art, Leisure, etc.
Then (painfully) link your thousands of categories to those top-level categories.
That way, when the user signs up, they can pick which of those handful of top-level categories interest them. Then you can automatically assign all related categories to that user (or limit it to a random subset if you don’t want too many).
I would then suggest that a feature of the application is that when showing content to the user, they can clearly see the original category and provide an easy option for them to “unsubscribe” if they don’t like that content.
Yes, it’s a lot of work for you in the back end, but that’s your selling point – you do the heavy lifting, so that the user doesn’t have to.