Why does it have to be a blood test? A cheek swab would be a lot easier on the baby.
In the US they can do it literally right after birth and a saliva swab is all thats needed. I guess if you were super set on a blood test they could do that right after as well bc they do the pku test and have to make a tiny cut on their heels to get a sample already. Donno if that'd be enough blood for a sample but idk why not
They do a heel prick test a few days after they're born, or maybe they do it straightaway in the U.S. I don't know... you could ask if they can do it then? Although can't DNA be tested just through a cheek swab? That would be much less invasive.