A fact is something that has actually existance, something that can be observed. The archeoptorix may have been a unique species, it may have be a one of a kind hybrid, it may actually be a lizard and a bird fossilized at the same place.
However, until you can reproduce lizards turning into birds or any other creature, you don't have facts to support the TOE.
If you followed that standard uniformly, you would have to throw out nearly all of science. No one has ever seen an atom, much less the protons, neutrons and electrons that supposedly make up atoms, or the quarks which allegedly make up those particles. No one has seen continents slide across the ocean floor and bang into each other.
I could go on, but the point should be obvious. Science-- all science-- does more than observe what can be observed in a lab. It draws inferences from those observations, formulates hypotheses, makes predictions, and tests if those predictions come true. If they do, we have a high degree of confidence in our theories.
We cannot absolutely prove anything in science. After all, maybe we are all strapped into chairs in the Matrix and the entire observed universe is a hallucination. But we can make very reasonable assumptions about the universe, which we hold with a high degree of certainty. We all do. You turn on the electric light in the morning without wondering whether the polarity of electrons has changed from negative to positive overnight.
People who object to the Theory of Evolution-- one of the best-supported of all scientific theories-- demand of it a degree of certainty they demand of no other branch of science (or, indeed, of any branch of human knowledge).
It is understandable why you do so. It threatens certain religious beliefs. Some of the popularizers of science (Dawkins is a particularly bad example), and some of my fellow FR evos, make this worse by trumpeting how Darwin supports their atheism. But there are many of us who accept the overwhelming evidence of the common descent of all life on earth, and do not lose our faith that evolution is a part of God's creation just as gravity and relativity are. Evolution is how God created us in His image.