With Mirena my side-effects were all physical and started right away. With NuvaRing, one of the side-effects (physical) wasn't right away, but was pretty early on. For the depression, I can't tell you if it started right away or not, because the depression steadily got worse the longer I was on it. It MIGHT have started right away and I didn't notice it because it wasn't so bad right away. I'm not sure. I was on it for almost a year before I made the connection. I remember several months where I was seriously depressed, but I just thought it was due to life things like my job sucking and stuff. I'm pretty sure I was sitting in my bedroom crying (not for any real reason, just because crying was something that happened frequently) looking up side-effects because of the other one I was experiencing, and stumbled across women talking about the depression they experienced while on it. It was like somebody had just slapped me in the face and yelled HEY! IT'S THE BIRTH CONTROL! I went in the bathroom, pulled it out, threw it in the trash, and never looked back.
I can say for sure I started to feel BETTER immediately. The next morning I woke up feeling better than I had in weeks and after about a month or so I just steadily started feeling better and better. After about three weeks I was on the Mirena, but I don't think it had anything to do with it. Just the further away I got from having those particular hormones in me, the better I felt.