This answers assumes the person making a secret base has some wealth since even hand waiving the tunneling for the secret base, would still cost a considerable amount of money to set it up and furnish it.
Frame Challenge: Buy an Old Mine or Build a New Mine
The technology proposed in the question is capable of also compressing other materials besides quartz. As such it is able to make precious gemstones like diamonds. So instead of trying to make a secret base in a random location, buy a dead diamond mine, or buy a plot of land in a more convenient location to build a new one. Then announce you have found signs of possible diamonds, and begin some exploratory digging to confirm it. Then scale it up to a fully operational mine, that instead of mining diamonds secretly makes them. An operating mine is expected to produce large amounts of spoil and so you no longer need to hide it.
The secret base would be hidden in part of the old mine or in a closed off section of the mine. While the rest of the mine looks legit enough to get past any government safety inspections.
Front Company
Having a front company allows for various types of cover for secret operations. For example no secret base is complete without minions. The minions could be disguised as miners and so would have a good believable cover for why they are coming and going from the base for whatever missions they have been tasked with. Diamond mines require security, so you have a very good reason for why you have armed guards around the mine.
Mines use a lot of equipment including some specialized equipment. So you have a very good reason why there are trailers moving unusual equipment in to set up your secret base with. Also you can tap into existing infrastructure without raising suspicions.