Your assumption that the ToE is based on an 'assumption' is incorrect. The evidence the ToE is based on comes from a variety of different fields of study, including genomics. This confluence of evidence leads us to 'conclude' that common descent is correct.
This is contrasted to ID which is defined by the assumption of its conclusion.
Well, there is probably no more point in debating this. I think you get my point, even if you don't think it's valid. The "confluence of evidence" is amassed to point to the conclusion that the investigators want to make. Sort of what a prosecutor does to try to convict someone that he thinks is guilty.
But that is not the same as fact. It is still based on guesswork and assumptions. But of course the prosecutor must convince himself that he is right before he goes into court, or he will probably not be able to convince the jury. Science provides some of the evidence for the prosecutor's case, but there is always the possibility that there is another explanation that no one has thought of.
Projecting backward into the distant past is guesswork.
If events A and B can be demonstrated in the lab to cause C, it does not follow that every time you observe C, A + B must have happened.