When you progress normally in the game until you reach Fossil Roo, there will be a miner picking the rocks. He will ask you if you want to have a go at it as well after trading him.
This is the same part where you can free the moogle out of the rocks for
This is your only shot at getting it, so it would be wise to have a second save, if you'd like to continue and do this later, as it turns out this is RNG. Because of that, I already have to start a second playthrough, since you cannot enter anymore (you can try, I did to find out the hard way) as the staircases leading down to Fossil Roo is being blocked.