I've had two babies and getting back to running after pregnancy is probably one of the hardest things post-pregnancy. I just had a baby 9 months ago. So, this is all still very fresh on my brain. I think with all things running you have to be patient and trust the process.
I started running again about 5 week after giving birth. I didn't have a c-section, so didn't have the same recovery period as someone that has a c-section. Below is my progression week-by-week for 8 weeks, I think the best part of coming back to running after being injured or pregnant is that the gains do come quickly! You can see by week four I was clocking in sub 10min/mile and by week eight I was doing sub 9 min/miles.
This wasn't a plan that I had pre-written but feel free to use it if you are looking for an 8 week plan. I went mostly by feel and took days off whenever I felt a little sore. I do remember the first few weeks my knees were hurting pretty bad due to the relaxin hormone still circulating through my veins. Check out the progression below:
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8