In essence, unless their background is specific enough to state, 'I never had a SIN', by default they had a SIN.
There's never a by default in Shadowrun character backgrounds.
Here's the thing: unless there is a specific reason - to wit, your mother and father both didn't have a SIN - when you're born, you're issued a SIN. This isn't 'default' for character backgrounds; this is default
for the shadowrun world.Now, whether that comes from being a poor SINless bastard in the Barrens or the Ork Underground (or other similar highly-disadvantaged area, like GeMiTo or the GlowPunks in the SOX) or being in a techno- and culture-phobic back-to-the-earth group such as a deep-woods NAN tribe or a tribe in the hyper-advancing jungles of Amazonia or living with the Abos in the Outback doesn't matter; if your mom (AND dad, if your dad is admitting to you) doesn't have a SIN and never manages to acquire one as she goes along, then yeah, you're never going to have one yourself. If, on the other hand she gains one - like a criminal SIN, or signing her life away to a corporation that issues them - and for some reason you get hooked into the system as a child (e.g. child protective services or the corporation), then ta-da, you'll get issued a SIN.
If the game is a street-level game of 'gangers everywhere', then sure, yeah, none of your characters will have a SIN - that's default
for that game. If your character background is 'I grew up in the Barrens', yeah, you probably don't have a SIN, 'cause your parents probably don't either. If your parents are shadowrunners, you probably don't have a SIN - again, 'cause they didn't. But unless your character falls into those actually-pretty-darn-narrow parameters, the character is going to have had a SIN
in their past - and this is something that has pretty much always been understood across the editions, and explored in a few places, such as 'Zoe', the reporter 'going into the shadows' in the 'Life on the Run' section of 3e's Sprawl Survival Guide. (Which also shows one of the thread-aforementioned standard ways of how to burn your old SIN - fake your death.)
I'm not saying every character
has to have a SIN, or has to have
had a SIN; obviously, a Barrens ganger is likely to
not have one (though a ganger from Renton actually
is ...). But unless your birth fits into that specific subset - '(neither of) my parent(s) didn't have one' - then the default of Shadowrun-the-game-universe is that you got stuck with a SIN when you were born.