Well, from watching mine building his burrow progressively, clearly he could survive with just 3". At first he just slided under a LR and push out the sand side way. He has been making the inside of the burrow deeper everyday. Clearly he prefer the burrow going straight down. As of yesterday, I could see the hole going straight down and he could float above his burrow and slide back down slowly every so often.
To keep him happy, I would really recommend get as deep as you can afford.