I would buy a half dozen of fairly inexpensive arrows (not necc "crap arrows), at the appropriate cut length and appropriate spine as he is he is set up now.

Once he grows a bit, bumps up his poundage, etc then buy new approriately spine arrows at that point.

IMO, trying to make one arrow spine a "band aid" to fit a multitude of poundage/lengths, is a bad idea. Get him the right equipment off the bat so that he maximises his accuracy potential. Success=fun & high interest. Frustration= kid off to find another hobby.

I got frustrated with a new bow recently trying to "make" a certain arrow work for me despite the fact I knew it was pretty borderline. Flight looked good, but the spine was a bit too weak and it showed up on the target..i.e. CHS (can't hit..you know what). Tried some stiffer arrows and groups shrunk from improved cylinder to arrows touching.