If you were not married to the father, the court order of support that you (or the state on behalf of your child) may request from the court can impose support beginning at the date of the child's birth. If you were married, the order may begin at the date of separation, but usually "temporary" order (in place until trial) do not go back to the date of separation, but rather reserve that issue for trial and decide on current/future support only.
If a support order is entered at some point in future and is payable through the state Divsion of Child Support AND orders back support, then he could request credit for funds he has paid you or things he bought for the baby, but it is his responsibility to prove by cancelled checks or other good, written evidence, that he did so. If all he is contributing is an occasional bag of diapers, it is not likely that he would be able to "prove" such contributions so as to provide him a credit for back support.
If it is your intention that he be given such credit, you should maintain a list of all items he provides, with the cost (and preferably also the receipts) and both of you signing to show that you both acknowledge each specific contribution of money or goods.
Be warned if you are receiving state aid, that his chances of getting credit against a back support judgment in a future child support order, would likely require the prosecutor (DCS attorney) to consent since the state is entitled to reimbursement out of child support, for amounts it spends on support of your child.