It should pose no problem, depending on the origin of the 7.62. G.I. brass is "thicker" than commercial brass and therefore, a little "hotter" when fired in a "commercial" chamber. If the ammo you purchased is reloadable and military in nature, most manuals recommend a 10% reduction of the powder load.
I have fired thousands of rounds of G.I. (U.S.) Lake City brass in my M1A, .308 M1 and Model 70 match rifles chambered for .308. I have one match rifle that is so tightly chambered, that it will only accept commercial brass, Winchester, Remington, Federal, etc. and to close the bolt on Lake City match requires excessive pressure on the bolt handle so, I just don't shoot L.C. brass or ammo out of that rifle.
I owned a Remington Mod. 700, Police model and shot several hundred rounds of Lake City M118, M852 and M118 LR ammo with great results and no ill effects. The barrel on that rifle was stamped ".308". It was and still is a tack driver and a friend of mine bought that rifle from me to shoot "F-Class" matches.
I have also witnessed individuals shooting 7.62 ammo out of Mod. 700 BDL rifles with no ill effects. A friend of mine had one, several years back, and forgot his ammo (conveniently?) when we went to the range to zero his rifle. His used some of my L.C. ammo and some R.A., Vietnam era ammo to zero the rifle with no issues. That ammo was "ball" ammo with the 147 grain bullet so, accuracy was about 1.5 to 2.5 MOA. He shot some of my hand loads that I use for matches (168 gr. Sierra BTHP) and the rifle produced sub MOA groups. The reloads I had were M118 match brass with IMR 4895 and Federal primers. There were no issues with my hand loads.
Great rifle and great caliber! Enjoy and remember to post a photo of your groups.