Taking a look at the Corpus of Contemporary American English, there seems to be an about equal number of
ascent of versus
ascent to. Examples from the corpus:
[...]an expedition in honor of the 50th anniversary of the first American ascent of Everest.
The ascent to Mountain Lake Lodge is a slow, winding seven miles.
I was wondering whether there is a sense or "process" when using the preposition
to, meaning an ascent that is perhaps not completed, whereas
ascent of would be preferred when referring to the actual conquest of a mountain.