When does your theory become fact/
-When a group of 'prominent' people espouse your theory/belief
-When certain regional 'academia' teaches your theory/belief
-When you have 'figured out' that the most reliable answer is the one coming from someone you respect.
Theories only become facts when they are acknowledged
outside the scope of science. Science does not decree fact.
For that matter, in scientific usage "theory" is a far stronger word than in popular usage, where it is treated as if it meant "hypothesis".
Some Creationists seem to believe that in science you may create "theories" basically out of a whim and have them become something more (fact?) once they earn enough of some form of prestige. That is really not at all correct.
Instead, science uses hypothesis that need verification by way of falseability tests. That usually means using the hypothesis to predict the results of experiments, then actually doing those experiments, often and by different, unconnected people if at all possible. It is not possible for an explanation to be a scientific theory without some degree of support from falseability tests, AFAIK.
If I am not mistaken, a theory that somehow turns up at some point to fail those tests must then be "demoted" to a hypothesis. Not sure how often that happens, if at all.
Your options are all variations of an appeal to authority, and therefore none quite serves for science, although they could be useful as reference points for a start.