Cave will be unlocked when you find the last part of the Mysterious diagram and build the City Gate.
When the Cave is ready you will open new levels in Treasure Hunt mode and find parts of Skystone.
It takes time to excavate from one set of ruins to another.
There are 7 available levels of the Cave and 125 match-3 levels to beat. To upgrade the Cave you need to fulfill the requirements. You also need resources to upgrade the Cave. Upgrading takes time but you can speed it up using your crystals.