Why is the Big Bang Theory considered a "theory" and not a fact?
We do not and cannot know that what is described in Big Bang theory actually happened.
In the natural sciences we make observations and construct models.
If those models are consistent with our observations then we can make predictions from those models and test them against more observations.
If some observations contradict our models, then we can tell that our models are wrong or in need of modification.
For example, Newton's laws of physics provide pretty good models sufficient in accuracy to allow us to calculate how to land a man on the moon. Are they therefore true? Not exactly. Newton's laws fail to work well at velocities approaching the speed of light. So we can tell that they need some adjustment.
Einstein's special and general theory of relativity provide more accurate models. So are they true? They predict all sorts of strange behaviour which we have actually observed. They seem to provide useful models, but they do not explain everything. For example, the extreme conditions in a black hole or those we think existed at the start of the universe provide some challenges to General Relativity.
From a practical perspective it is useful to operate within theoretical frameworks that we treat as facts. We need to make assumptions in order to reach substantial conclusions. So we often act as if something like Big Bang theory is a fact, but we cannot know it to be so.
Essentially in any natural science we cannot prove anything to be true. We can demonstrate that theories are false. This is the honesty of science.
Consider an alternative theory: The universe and everything you "know" actually started
You may protest that you remember what you did yesterday. In my theory I can explain that these are simply implanted memories, not real. What about radiometric dating? What about the Andromedra galaxy being
There is no way to prove that this theory is true and probably no way to prove that it is false.