OK, you've got some Euro? .30-06 military fired brass.
First step, make sure they are NOT Berdan primed! If they are Berdan primed, toss them, don't bother trying to reload them. Get a good light and check. One central hole in the primer pocket, we move on. 2-3 small holes, off center, toss the brass and get other stuff.
If it's military it probably has a crimped in primer. This will have to be dealt with, before a new primer can be inserted.
7.62x63mm is the European designation for the .30-06. The .30-06 was never a popular sporting round in Europe. There is commercial 7.62x63 ammo but it is scarce and its unlikely to be found in the US. And, it might be Berdan primed, as well.
Several European countries used the .30-06 in military arms in the years after WWII and before the adoption of the 7.62 NATO. Some were US supplied guns, some were guns they made themselves for the round. 7.62x63mm military ammo will be Berdan primed. And therefore, not practical to reload.
DO NOT run a 7.62x63 case into your .30-06 sizer die, until after you know if it is Boxer primed (the US system) or Berdan primed (the European system) Berdan primed brass WILL BREAK your decapping pin, and worst case, might bend the entire decapping stem.
Check that brass you have, and get back to us. If it's Berdan primed (and I highly suspect it is) differences in case thickness etc are moot.
Do understand it is not impossible to reload Berdan primed brass, it is just impractical, because the new Berdan primers you will need are very rare in the US, and standard US loading dies and tools won't work to decap fired brass.
If the stuff you have is boxer primed it would be pretty rare, but if it is, you can use it and we can discuss the tips and tricks to loading it for you new rifle. If its what I think it is, (berdan) it should go in the scrap/recycle brass bin.
Good luck, and please, do let us know what it is.