Sure, taking the average could be an option. But the key point is that the Two Tower can alltogether do without the user id (where the Matrix Factorization cannot)!

Maybe there are certain things you know about your users up front, that they share with you during registration. It might be their age, their interests, etc.

Two Tower allows you to represent your user as these features! In this regard, no training is necessary and you are ready to serve recomendations for the user from the get go.

You could still train with embeddings for user ids and take their mean for new users, or you could only have a model that would represent the user via its features (like discussed above), or you could have a combination of these two approaches or do still something else (for instance, train with a class of "unknown user" where you would sample examples into that class based on some criteria). Two Tower gives you the flexibility to pick the option that would work best given your situation.

If you train without users ids you shouldn't need to do anything extra at inference, but other approaches might require an additional step or two.