From what I gathered, your 5 years in the US starts counting when you get your citizenship. And another way is applying for a tourist visa for your son, if they see all the family have access to the US they won't deny him. Secondly, for an expedited case hardship waiver.
I think the OP is really in a pickle here. As ban for IV from Nigeria is coming up, it will take a while to get a visa, if one is even granted with a waiver (probably on the more likely side considering its an infant). But on top of that if they dont get a visa for the son within the next 6 months the visas for the other family members will expire
OP your wife may need to enter the US to activate her visa and return to Nigeria and hope that the son will get a visa quickly.
