"vast mountain" is correct and usable in written English.
You could use it to refer to an especially large mountain. For example, "The sun was rising over the vast mountain, filling the sky with a beautiful pink hue."
There is, admittedly, a vast mountain to climb.
We see piles of combs, shaving brushes, shoes and a vast mountain of human hair.
We emerged into the blinding brightness of a vast mountain valley desolate save for our train's lonely track as it descended onto Lake Baikal's northern shore.
Kluane National Park and Reserve, in full Kluane National Park and Reserve of Canada, vast mountain wilderness with extensive ice fields in southwestern Yukon, northwestern Canada.
Despite its vast mountain ranges, fossil-packed rock faces and rugged beauty, Kyrgyzstan has struggled to secure a reputation as a first-class climbing destination.
Cypress also has a Nordic Area dedicated to cross-country skiing and snowshoeing, again offering incredible views of the vast mountain ranges north of Vancouver.
Alaska's vast mountains are reminders of infinity.
Television pundits bring vast mountains of expertise and wisdom to a discussion of the Iowa caucuses.
On all sides were vast mountains topped with snow and skirted by emerald forests and vivid blue lakes.
I had heard tales of British Columbia and her vast mountains, and of the icy northern provinces, but they remained abstract regions in a vast country that I half called home.
Captain Cook had appeared to settle the matter in 1774, when he noted the existence of "firm fields and vast mountains of ice" making passage to southern latitudes beyond 71 degrees near impossible.
