A lot of MA schools test for the first belt or two quickly. That shouldn't be a red flag. What should be a red flag is if EVERY belt is awarded every two months. My CI usually skips the first test and double promotes adult students (if the pass) when they're supposed to take the second belt test because the syllabus for the first test is pretty small. He's supposed to go white-advanced white-blue, but rather than testing them 2 months after they start and then again two months later, he usually just waits until the 4 month or so mark and tests them then for both ranks.
Judo is kind of a wild card in this though, as people can promote due to competition success. People have gotten to black belt very quickly due to competition. I don't know the specifics, but I've read that if you beat 5 consecutive black belts in a high level competition, you'll be promoted to black belt. I'm sure there's more involved, but it gives you a basic idea. And I think that's far less common today as it was a few decades ago.
Judo is very standardized, so I wouldn't worry too much.