Congrats on the cutie!
I just got my BTS a couple weeks ago and they are quite the characters. If you haven't seen it already, there is a good video on youtube (by LLL reptile) of mixing up skink chow. I think I searched for "blue tongue skink diet". Very good information.

My guy seems fairly picky, but he will eat his skink chow and apparently loves pinkie mice (f/t).

Good luck with your little guy!