I personally believe that it's due to the chores. At some point, they noticed that Harry has problems with doing his chores (cooking, gardening...) that are consistent with very bad vision, and reluctantly gave him glasses (perhaps asked for them from some friends) so that he could do the chores better.
It is also possible that the glasses came with the original Harry package back in 1981; presumably James and Lily could have guessed that their son might have had bad vision (certainly Dumbledore would know enough to guess that). Perhaps, at some point on or before the 1st of November, 1981, glasses in normal two-year-old size (or even a bit larger, if they were intended for future use) were bought for young Harry; with how tiny Harry was by age eleven, the glasses could easily still be just barely fitting (it is mentioned that they are by then too small), and once in Hogwarts they could probably be adjusted magically.
Going on from that... perhaps Mrs. Figg got him the glasses (at some fairly early point, perhaps around 1983). It would certainly fit both the timing, and her. I'm surprised I didn't think of this idea earlier.
From my own experience... my memory tells me that I wore the same pair of glasses from 4 (or even a bit less) to 7-8 years old, and that a pair bought when I was about 5 was stolen when I was 14 (by which point it was a secondary spare, but still useful, and only secondary because it didn't fit my worsening vision well). Based on that, it would have been very possible that the glasses were bought before school (or even earlier); I suspect my fairly small size at young ages (in particular, my weight at age 11.5 was 27 kg) is a good approximation for young Harry.
Note that Harry had successfully learned to read, and indeed did not seem to have any problems reading while in school (which he would've needed to do much); otherwise he would've had trouble ever getting higher grades than Dudley, since so much of the school system depends on being able to read. This makes it likely that he got glasses before going to school; either by 1981, for chores, or perhaps in preparation to school (though, again, I guess it's possible that he'd already learned to read by 1981 anyway, and it's unclear exactly how much were the Dursleys non-caring for him while he was still a baby).