Depends of the era. From the Xth up to the XIIIth century, these people would have knights if they entered under a noble service, or eventually with a military order.OK, so it sounds like there's consensus that at the very least men of low or foreign birth who served as bodyguard (mainly for merchants and other non-lords, I assume) who could afford to pay or feed them. Is that about right?
After that, it's probable that they'll join up a with an urban militia or a mercenary company, simply because there was far more employment.
That's a particularity of feudal institution that is to be understood : milites had a technical monopoly on this sort of things, it was as well their social role than social justification, even if it began to crumble after the XIVth.
Individual "sellsword" isn't unthinkable, but would have been extremly exceptional for the time, as it would be concurrenced by a far more widespread and "popular" (as it allowed social ascencion) use of feudal institutions.
A bit far-fetched maybe : merchants heavily relied on existing features for their protection (as the Counts of Champagne guaraunteed the fairs with Garde-Foire).If so, how plausible is this scenario? -- a boy/young man ends up stealing among a band of bandits, but eventually leaves the group, deciding there's more job security in protecting merchants from people like his former comrades. (Mind you, he likely won't go bragging about this backstory, so even if it could have happened, it'd make perfect sense if there wasn't a recorded instance of it.)
If a merchant was to enter in a dangerous zone, he would probably find people issued from urban militias (from which several companies were issued as well) or from its protector.
That said, I can see a boy/young man gaining the affection of a merchant and ending to be made sergeant at the service of the merchant or merchant's corporation. It would be an unusal way, but could work. It's far more police or guard work than mercenary, still.
Now, if you want to "mark" the destiny of your young man/boy as exceptionnal, it could be useful to begin with that.
I don't think it counts : Varangians were organized collectivly, and newcomers joined it rather than selling their skills on their own.The Varangians, for the ERE