It is extremely easy to "prove" evolution via common descent to a young earth creationist. When they ask how you know it is true, just say you read it in a book (or 66 science books). Oh ... did I mention there is also a tradition about evolution that goes way back?
When I reflect upon evolution via common descent, I have this "sense", I call it Sensus Naturalititus, that it is true. This sense remains even when I consider the defeaters for evolution.
I have also had amazing experiences of evolution. But I don't wish to discuss it, because it is very personal.
Some say there are "contradictions" or inconsistencies in evolution. I say, these people are not open to harmonizing these issues.
Sure it seems silly that we came from a pond scum. But I ask: "Were you there?"
Some day, and we don't know when that day will come, EVERY tongue will confess that evolution via common descent is true. Woe to those YEC's on that day.