Excavating the Mines of Moria

[Tuor in Gondolin]

It's also possible that the mines began as part of a large natural system of caverns

I think that's a good part of an answer. Another, depending on the
quality of stone and other material, sold or given to Gondorians for their many
building projects in Gondor and Calenardhon, if not as facing, then
as filler. Btw, why not employ dwarves as builders/co-builders of
some of them---think Gimli after the War of the Ring in Minas Tirith
and the Caves of Aglarond.