It helps if you have the original inner sleeve, to see what contemporary albums were being promoted.
There may also be clues in the deadwax, depending on which pressing plant manufactured the LP. I am not familiar enough with A&M pressings to offer more details than that.
I will say, if you are fortunate enough to find an A&M record with either a delta/triangle in the deadwax, or an "MR" in a circle, you have a west coast Monarch pressing, which was presumably cut from the first generation master tapes. Other plants around the country were likely provided tape copies.
Regarding the runout groove markings, there is usually the main matric number, for example, A&M 4159 - it might say SP-4159 - whatever the label matrix number shows. That's the one in parenthesis on the label.
Following that, there's usually a stamper designation, like 5 E or 2 J or something like that. It would be my own interpretation that the lower the number, and the close to the front of the alphabet, the nearer you'd be to a "first pressing". But that's just a logical assumption on my part.
I've seen promotional albums that have numbers seemingly too high, so my theory probably goes right out the window. I've noticed a number of A&M records that have designations of "RE-1" or "RE-2". It would seem to indicate a revision of some sort. Perhaps a fix to something following a test pressing (?) Don't know.
Steve makes a good point about the album jackets. But beware, as some shops or sellers might be swapping good records from poor jackets into nicer ones.
Back when I was purchasing all of my TJB vinyl, I came across a sealed copy of Volume 2 with the original rear illustration. I opened it to see if it had one of the early A&M labels or not. No, not a 12 o'clock logo, but still neat to play something that old which had remained sealed.
That's another point, in terms of the record itself. If the earliest A&Ms came on a cream colored with brown printing and the A&M logo at 12 o'clock, that would be the earliest of pressings. (My spotless George McKern LP has this label.) And for a while, after A&M settled in on the tan label with white/red logo, the logo still remained at 12 o'clock. On later records, after the label changed to the 9 o'clock logo, you may notice that the type face of the album title and artist was still tiny at the top--this typesetting was left over from the early 12 o'clock logo days, only it was printed on the newer labels.
I think Peter Frampton's "Frampton's Camel" (1973) was the first to have the A&M Records new swirl logo. The first A&M swirl that I saw was back in April of 1974 when I was 8 years old & when I saw the 45 single of Sister Janet Mead "The Lord's Prayer" at "National Record Mart" during a trip to Greensburg, Pennsylvania at the old demolished "Greengate Mall" to see my late aunts, late uncle & relatives.
The switch from ochre to light gray labels happened in mid 1973 as I recall. There's not a exact point along the catalog number order that sets this. The first Ozark Mt. Daredevil's album, SP 4411, had the new label. The old label appears on SP 4413, Booker T. & Priscilla's CHRONICLES. Projects weren't released according to the catalog number assigned.
I'm not sure, but I think the first one I had my hands on with the silver/gray label was the T.J.B. You Smile album, or possibly the "Fox Hunt" single from that album. But, it's been tooooo long... I might be wrong on that. (You'd think something that momentous would be burned in memory!)