C.M.
I just joined this group and it strikes me as funny that the first request that came up on my screen was yours. I have never met anybody on line and do not belong to any groups/blogs/etc. my time on the computer is pretty limited in general however, I do happen to be a pilates instructor and also a runner. I also had a C-section 4 years ago.
In response to your questions, yes, there is hope :) It has only been one month! I will speak on behalf of many of my clients (my story is a bit more difficult). It is hard to put a specific time on it, but you will know when you are ready to start working out again. In my opinion running and Pilates is a perfect combo to get your tummy back. Yes, it typically is a bit harder and does not come as easy as it used to, but if you are willing to stick with it and work hard, you will get it back.
The only obstacles that I have seen to interfere are a lot of stretch marks, diastasis of the abdominal muscles, and rare, but possible umbilical hernias from the C-section (that is what I had).
Just relish in beauty of your new baby, and know that you will have your body back. Take your time and let your body heal.
I hope this helps.
C.