When the first Apple IIe systems shipped in January 1983, the sticker on the bottom displayed an A2S2-XXXX serial number just like the Apple II Plus. The typeset of the serial number looked just like the early Apple II & II Plus numbers (see S/N 1601 below...this is Mike Maginnis' system). It seems that soon after its introduction, a "1" was printed in front so it now read 1A2S2, presumably to avoid confusion with II Plus, and the number itself was printed in much larger, blockier text (see S/N 9761). Following that, the label was changed so that the extra "1" was now part of the label, but the serial numbers were still sequential (S/N 76667). Finally, I guess since production was ramped up to such high volume, the numbers switched over to a date code (last image).
I wonder when Apple made the switches along the way? Interestingly, I have a system with the "1st state" label in the 11,000s so that means when they switched to the 2nd state (with the amended 1A2S2 designation and blockier digits) they may have the reset the numbering back to the start as well.