You're probably looking for a needle in a stack of needles, but you never know if you don't try. I would start by looking at the lock and tang dates to see what year your piece was most likely manufactured. This will probably indicate a ballpark guess as to what time period you should be searching. Other markings on the barrel, lock internals, or other parts may indicate a certain inspectors mark that just might be identifiable to a known inspector working at the Springfield arsenal within a certain time frame. Since these were never serialized, you'll probably hit a dead end there.

Since you have initials, you might want to check within online muster rolls, service records, pension records within second corps beginning at the possible manufacturing date of your particular rifle. You'll probably find more than one, possibly a few with those initials.

There were probably a million of these things made during nearly four years of the war. They were maintained in inventory beyond that in surplus and state arsenals even after being replaced by the M1863. It may have been issued to multiple service members as people served out their enlistments, were killed, wounded, or possibly even captured. It's probably best to just imagine the possibilities as you enjoy it for what it is. Good luck in learning more on it.