Well, the Romans also used Carpenters for building things on Stone, only that wood is much harder to preserve.

In Spain multiple big ferris wells were found in mines and also some parts of machines that were using to pulverise rock. There were machines for hammering the rock using water, made in wood.

The Romans probably used machines for polishing the stone also so it could fit with other stones, as they did everything this way and those machines were done also with wood.

We also know that they had machines for lifting the enormous rocks as we can see the marks that the gripper left, done in wood.

And every arch done in Stone needs to be build first in wood. The romans loved to use the same arch so they could reuse the wood. The romans standardised everything so everything could be reused or mass produced.