A theory is only ever provisional, and it is based on an assumption that observations are not illusions. There is no other basis on which to progress with the use of evidence to determine whether something should be called a fact or not.There are many kinds of evidence in the world.
The question of existence can be considered a separate discussion. But if there is an intersection I imagine it would be in that if you know a thing exists it is either evidence of something else or there is evidence to prove that it does. But we don't have to talk about both or either of these.
We can talk about existence. But in what sense?
If you have evidence for something can you form a theory about that thing?
Stuart