Pick up a FIELD gauge. Might be hard to find one. That's militarily used to check in-service chambers - that fail the No-Go. You can still run a military rifle that fails No-Go, as long as it doesn't fail the Field Gauge. Once it does, it gets re-barreled.
However, as SS stated above - find out what chamber the barrel manufacturer cut in that thing first, or you'll chase your tail on this. If it's truly a .308 Win chamber, and not some hybrid chamber, then find a Field gauge.
EDIT - for clarity, finding a 7.62 NATO Field gauge might not be that hard. Find a .308 Win Field gauge might be tough...