The veracity of scientific claims is bolstered by successful predictions. Newton was verified by the appearance of Halley's Comet on schedule. Darwin estimated the amount of time required to evolve from a single celled organism to the observed variety of multicellular life. He noted the current rate of variation and estimated several hundred million years. The correct number appears to be 500 million years.
It's pretty striking that an estimate derived from a biological theory turned out to be closer than the prevailing estimate provided by the physics of Darwin's time.
I think the principal point to be made about the age of the earth is not that it somehow "proves" evolution, but that it was originally raised as an objection to evolution. Darwin's detractors said, in effect: "Very nice theory, Mr. Darwin, but the earth isn't old enough for all that evolving, so that shows you're wrong." Well, so much for that objection. (Except for the YEC gang, but they're totally nuts.)