o dear where is the prof
a very technical point is: look at the phase diagram for water
the ice/liquid line has a negative slope
this means as you compress a system ( whether or not it is incompressible ) then the temperature of freezing goes down .....
so in that system you are still gonna have to remove heat
this answer is even more technical
https://www.reddit.com/r/askscience/comments/2nfeix/if_water_is_compressed_enough_would_it_turn_solid/
BUT BUT BUT
the idea is OK
the Brit Mus has a show on mughal jewellery featuring hard stone chased with gold - and THEY said that with a needle point, the gold was compressed into the fine crevasse in the hard stone and by reason of the above, would liquefy under the needle point - and so you could inlay / chase gold into a hard stone.
( well you could see that you could achieve that because the object is there to examine but that is how they said it was done )
some pretty spectaular examples here but not much inlay