Can I collect child support from the date my child was born?

In Michigan, that's a myth.  The answer has been no,  for several years. Here's the specific law:

 

552.603 Support order; enforcement; information to be included; notice of new information; service of notices or other papers; accrued interest prohibited; failure to comply with requirements; fee; admission into evidence.

Sec. 3.

....

(2) Except as otherwise provided in this section, a support order that is part of a judgment or is an order in a domestic relations matter is a judgment on and after the date the support amount is due as prescribed in section 5c, with the full force, effect, and attributes of a judgment of this state, and is not, on and after the date it is due, subject to retroactive modification. No additional action is necessary to reduce support to a final judgment. Retroactive modification of a support payment due under a support order is permissible with respect to a period during which there is pending a petition for modification, but only from the date that notice of the petition was given to the payer or recipient of support.