It's going to vary a lot depending on your natural athleticism, size, how aggressive you are, age, etc.
But generally, I see people start to really enjoy BJJ at around 6 months (again, a lot depends on the person and his circumstances). For some guys, it's the first time they don't feel lost when rolling.
They may not feel they are progressing against the regular training partners (who are also improving), but find the newbies are easier to handle. By 8 months, many are starting to develop a set of techniques that could be considered an A game.
I see guys begin to make moves work without muscling it or the other guy making a big mistake. In other words, for the first 6-8 months, guys get a submission or a sweep, but they have to spaz to do it. After 6-8 months, they are starting to develop the sensitivity to pull off the move without brute force. As a result, they can roll longer and smoother without gassing out.
If you are feeling these things happening, you are doing great. If not, they will come as long as you train smart and just have faith in the techniques, don't rely on strength. Be sure to ask more experienced training partners for pointers when stuff doesn't work and focus on drilling carefully and not just being on autopilot.