My Garand does the same thing. It was one of the last M1's made at Springfield, (#5,9XX,XXX) and is in excellent condition.
The first round goes 2MOA low & 2MOA left, and then the next seven rounds cluster together 2MOA higher & righter. I've learned to live with it by "holding off" on that first shot, (when I usually have a little extra time to do so), and then holding "normally" for the rest of the string, as the pace usually picks up. I've fired five en-bloc clips in a row (without "holding off"): I got a nice tight 5-shot group located 2MOA low & left (where all the first rounds went), and a nice 35-shot group in the center of the target. If I load single rounds, one after the other, during slow-fire practice, each and every round will land 2MOA low & left (unless I remember to hold off, or dial in a couple of "Up & Right" clicks beforehand).
I've always figured that it has something to do with the way rounds #2-7 get loaded automatically. But, I've never pushed on the op-rod after chambering the first round, as was mentioned by Bart B. I've always just allowed the bolt to slam forward normally, sling-shot fashion. But, maybe I'll start pounding on it the next time. It might actually help with my first-round-flier problem (HA-HA)!
I did install a Wolfe "extra power" op-rod spring. It didn't help with the first-round-fliers, but, it did increase the pain associated with the occasional M1 Thumb (ouch)!
Watch your top-knot.