With science. Because God by definition is outside of nature and not subject to its laws, but the formulator of them. Therefore efforts to get Him to do lab tricks for you based on the idea He must behave in a repeatable manner IOW His own natural laws is nonsense. Fortunately there are other methods of determining truth outside of the scientific method.
And mathematically, you can. Does that in itself mean that it happened? No. Does that mean that this event can be detected scientifically? Joshua would say “no” and I would say “perhaps, but not necessarily”. The point here is that there is nothing unreasonable, by the math, in believing they are in everyone’s family tree somewhere, if they existed. Getting them into human history requires more, but showing that it is possible and reasonable to believe they were does not. And I say that as someone who does not see the theological necessity of GA.
BTW there is a lot more evidence outside the mathematical model that they were there, but you can’t “prove” it by science. You can only point to anomalies in human history which are consistent with that hypothesis.
As for the “talking snake”, you should look at the Hebrew. There is a whole lot more going on there than that.