TTC after birth

Hello! I know this will sound crazy but I just had my sweet baby girl match 6th. Today I started my first period since birth! While I am excited because I now have a chance of getting pregnant again( yes I know I could have right after ) but I am now able to keep up an track it. I got preg 6 months after my first pregnancy with my second daughter and I’m hoping this time it is sooner. My husband and i are TTC I did want to ask some questions so

- what is the soonest you personally have gotten pregnant after birth ?

- are the chances of getting pregnant higher because I just had a baby or is that a myth?

- I am not breastfeeding but my milk is still coming out is this bad for ovulation?

(Please don’t tell me Doctor advice for getting preg again )