While it is certainly possible to get decent accuracy from retro rifle parts, the design itself is not inherently designed for match shooting or long-distance sniping. It was designed to shoot minute-of-man at normal combat distances.
Just some of the factors that will negatively affect your groups:
--That slim pencil profile is nice and light, but very susceptible to heat effects. As the barrel heats, the point of impact will change.
--That GI chamber is reamed to a miltary 5.56 NATO spec. It's not likely held to the same standards as a quality match barrel.
--Those triangular handguards are retro-iconic, but the barrel is not free-floated. Any pressure on the guards is transmitted into the barrel and will be seen in the printed group.
--The standard fire control group is reliable enough for combat, but the trigger has its limitations. A good smith can tune one quite well, but most military triggers are creepy and heavy and rough (oh my!).
--The rifle is lightweight. Your every heartbeat will bounce that front sight post.
--As someone else mentioned, many components that we use for retro builds are used surplus of questionable background. They may last a long time, but they do wear, and excessive wear is anathema to accuracy.
--And if you enjoy shooting the old rifles as much as most of us here, you'll burn a lot of ammo so at some point you'll probably start buying the "cheap" stuff. Now some of the cheap stuff is perfectly fine for plinking and everyday shooting (I shoot a LOT of PMC Bronze through my retros), but it's not match ammo. Heck, even the military specs for M193 (55gr) ammo only had a requirement of 2 or 3 MOA, if I recall correctly. (Someone will be by with the right numbers, I'm sure.)
Put all that together, and you'll be lucky to average better than 3-4" groups at 100 yds. Carefully pick the best-condition parts and use good quality factory ammo, and you might see 2" groups. But it takes some serious retro-smithery and careful load development to get authentic A1 parts shooting anywhere near 1-MOA.
Of course, there's a lot more than accuracy going for these things. They're lightweight, they're historic and they turn a lot of heads on the range.
But in most cases, accuracy is just "ok."
If you can live with that, though...brother, you have come to the right place!
Post photos as you go and feel free to pick the collective brain of this sick little hive!