Well, your chances would be reasonably good if you were caught young and made a chorister. Choirs were unisex, and so the ones that weren't of cloistered nuns needed boys' soprano voices. These were a feature of a number of churches and cathedrals, and singing in one would have required training. Each vocal line in the polyphony of the time would have been taught by a solfege-kind of system now called the Guidonian Hand. Instead of reading from music books, he would have had to use this to memorize his part, and so a boy with a good ear and a good voice and a good musical aptitude could well be noticed .

And, of course, when he hit adolescence, he'd have to become something other than a soprano voice. He'd have to start directing the choir, writing new music, looking for a patron. So, it's not surprising that there are English composers of the 16th c. who are known to have started as choristers, like Thomas Tallis, who began at the Chapel Royal. Maybe the son of a farmer, but as little or nothing is actually known about his origins, his family was likely not upper class. William Byrd, whose family seems to have been more important, may have started at St Paul's Cathedral before moving to the Chapel Royal. But there are plenty of composers that may have begun in this way -maybe most of them- and we just don't know about it, like Hugh Aston.