To get to Mt. Fuji from Hakone, first, go to Gotemba.

From Hakone to Kawaguchiko Lake:

From Hakone Yumoto
Hakone Tozan Bus L line→Gotemba premium outlet→JR Gotemba station→Fujisan Station
From Gora
Hakone Tozan Bus M line→Gotemba premium outlet→JR Gotemba station→Fujisan Station
Odakyu Highway Express Buss→→JR Gotemba station→Fujisan Station

Fujisan Station (Mt. Fuji Station) on the Fujikyuko Line is a hub for Mt. Fuji sightseeing. A large red torii gate stands at the entrance and Mt. Fuji can be seen in the backdrop.

Tried to climb the mountain?
There are many viewpoints you can see Mt. Fuji in Hakone.

DL Mt. Fuji Viewpoints in Hakone
https://hakone-japan.com/pre/wp/wp-content/uploads/mt.fuji-viewpointsinhakone.pdf