I want to see how this goes in court when people can't test paternity for months. You see it makes a decent headline but is neither applicable nor effective for government or citizens.
I'm pretty sure this is just another step to make miscarriages punishable. If they can wrangle zygote personhood they can make any abortion both illegal and murder. They can then try to punish any women who miscarry.
Babies aren't tested the minute they're born. They get tested some time after birth and the father then owes the back child support. It would be the exact same thing, except the father would be on the hook for an extra 9 months of payments.