At best the serial numbers would be inside the lid in grease pencil. Later they did put serial numbers on some of the boxes, but that was not the norm. The number could also be found on a tag on the end of the crate sometimes, but that was often a condition and identity tag which was merely stapled to the end.
The odds of matching up a surplus crate with a rifle is very very low. Of the 20,000 produced by 1946, the remainder were either torn down for parts, destroyed, or still remain in service. Only a couple of batches of a few hundred are rumored to have ever been sold off, along with some very small releases through various unit shooting clubs. So at best maybe 500 original rifles were released.