Will it be correct to say that even before Darwin and Wallace came up with the idea of natural selection, biologists already knew the fact that evolution happened, and that it was only the mechanism through which evolution took place (for example, natural selection vs. Lamarckism) that was under dispute?

Or did Darwin discover the fact of evolution as well?

True

It was well known that evolution occured and had been since antiquity. What was missing was a mechanism/mechanisms.

Lamarck proposed the first integrated theory in 1809 which built on soft inheritance, which had been around for some time.

Darwin and Wallace added the idea of descent with modification and Mendel added a mechanism. The characterisation of the gene as the unit of selection came later and multilevel selection later still.