Burrowing is a Blue Tongue's natural behavior, especially for a new Bluey. I hardly even saw my girl for the first four weeks I had her; they all have their own personalities, so they'll adjust differently. However, your guy might adjust faster if you refrained from digging him up. I know it's hard because they're so cute and cool, and you just want to play with them
, but in the long run, you'll have a much more confident (and therefore calmer) skink if he knows he is able to be seen and hide as he pleases. I don't think uncovering him every once in a while to check on him will hurt anything, but I wouldn't recommend taking him out every time you do - he needs to know that your presence doesn't mean he has to be social. All of this will, in time, make him more comfortable and he may burrow less. As an even bigger incentive to come out, try giving him a little slice of banana or a blueberry when you see him aboveground; this worked really well for me. And for regular feeding, just place his dish of food on his cool end; he'll smell it and come out when he feels comfortable to do so.
Just to troubleshoot, make sure your temps are at around 96F in the basking area and 80F at the cool end and that your humidity is between 60-70%.
To stop the substrate from getting in his eyes, try using a either mix of Eco Earth and Repti-Bark or Cypress mulch or completely switch to one of the latter two. He'll still be able to bury up in it, but it'll be a little less finely granulated throughout, so it should at least make less of it get in his eyes.
Do keep in mind, though, that there is no way to stop him from burrowing - like I said, it's their instinct. This time of year, they are also more inclined to hide and sleep longer. Not that you would ever do this, but as a word of warning: Don't remove or lessen the amount of substrate below about 2". This will lead to a very stressed animal.
Hope you're enjoying your new little buddy!