I'm not really sure about your child support rules/laws but i do know where i'm from that the non-custodial parent (no custody) can be filed for child support you should look it up go to dss!!1 they'll know or can give you a number so you can find out
Of course you can. First you file, then the courts go to establish paternity, once dna has been established then you go in for child support hearing, usually this is followed by some ludicrous claim of the other parent for 50/50 custody. (They do this because it's a way to get out of paying child support.) Then a visitation and custody hearing follow. It may be easier for you to get your custody ducks in a row first. Make sure you understand the three types of custody laws for your state first. They are Legal, physical, and joint.