It wasn't accepted so easily at all. Multiple evolutionary studies concluded mutation is sufficient to explain the majority (if not all) of variation seen in a species.

This is further supported by historical studies showing consistent mutation rates overtime. There are different mechanisms that result in population wide changes, but that doesn't exclude random mutations (in the general sense, be it point mutations or transpositions) from being the progenitor of all new genetic information.

In what way does it not seem credible?