Does having partial custody lower child support amounts? Would my husband as the father be able to fight for 50% custody and win it even though he hasn't been in the boys life for the first year of his life?

Support is set by specific local rules ( state law in the US)
In Georgia for example, it is based on income and number of days each parent has the child based on custody. So yes having joint custody and having the child more would lower support.

Next not being involved for the first year won't help but you file, see what you can get, and then look latter for more if you prove you are doing it for the child.

But to be frank, if the only reason you want custody or visits is to lower payments, not because you want to be part of the child's life, don't,