How soon can u get a blood test? to see whos the babies father?

So my ex bf wants a blood test to be sure... I don't have a problem with him wanting one.. but I'm only a month pregnant... I'm not sure how soon they can test to see if he's The father (which he is, he's just being cautious or a dick!) Soo how soon can u find out? Do u have to wait till the baby is born?