Great question, Cassie. Unfortunately, the answer is not so great. And I'm saying this as someone who got into SAG (before it was SAG-AFTRA) that way!
Before I joined the union, I was cast as an extra in a feature film. The producer and director were still trying to fill one last principal role, and so they took a look at the interview tapes that the background casting director had made of us. The director liked my "look" and brought me in to read for the principal role and I got it. But, that was a very big stroke of luck!
It just doesn't happen very often. Let's take a look at the different mediums.
Feature Films: The roles are cast before the film starts and the director has a "shooting script" with all the parts. That will rarely change because it means that they are going to add a role that is not in the script to begin with. Rarely, but sometimes, a director will get the idea on the set that he wants a non-speaking actor to say a line. Example - a friend of mine was doing a bit part (background with a specific bit of action). He was working in a lunch wagon and was supposed to simply hand the star a sandwich that the star had ordered. However, the director decided it would be more natural for my friend to say "You want anything else with that?" after he handed her the sandwich. Boom! Instant upgrade and SAG eligible. (Ironically, the scene was cut from the final edit, but my friend still got his upgrade and SAG card.)
Television Shows: Upgrades pretty much never happen. TV shows are on a very tight schedule, and there is rarely, if ever, a deviation from the shooting script. Because time is so tight, the director will usually stick very closely with the script and not make changes. Possible exceptions might be on a sketch-type show, or if an actor has been a long-time extra on a show and is finally given a line.
Commercials: This is usually the best place to get an upgrade. Although still rare, it does happen more often than on films and TV. This is because you don't actually have to say a line in order to be upgraded. All that has to happen is that once on the set, the director decides, because of your "look," he wants you in the foreground where you are recognized.
A tip - if this happens on a commercial, ask the second AD about getting the upgraded contract right after the shoot, while you're still on the set. Yes, you could still get downgraded or cut from the commercial, but it's always better to get the new contract right then instead of waiting to see if you are still a principal when the commercial airs (because it might not even air where you can see it). It's often a big hassle to get the upgraded contract after the commercial airs. Besides, even if you are cut in the final edit, you're still owed principal pay for the shoot.
Web Shows: This can be another place to get an upgrade, but the show must be working under a SAG-AFTRA agreement to begin with. Some web shows are very tightly scripted and some are very loose and improvisational. The latter type will increase your odds of an upgrade.
Final word of advice - never, ever, say something (even one word) without being told to do so by the director. In order to qualify as an upgrade, you must be directed to say that line (or word, whatever). Shouting out a word or two while you're in a big crowd of extras will not get you an upgrade and could even get you kicked off the set.