Correction, they are a nation which calls itself "Israel". Anything more than that is unprovable, i.e., "they are the Israel of prophecy". You can call yourself a tuna sandwich, but that doesn't make it true.
Um, didn't God ordain that this nation would call itself Israel?
Therefore we must conclude that it is God's will that they call themselves Israel, isn't that true?
And if God did not want them to call themselves Israel, do you think they would now be called Israel?
Or do you believe that God did not have a hand in establishing this nation called Israel?
That's ridiculous. There is genetic evidence of their being Israel/Jewish. They've been using the technique to identify Jewish communities.
You honestly don't think those people disappeared after 70 AD, do you? You can follow them in the pages of history. They use the books of the Jews, the methods, the traditions, etc.
Besides, you avoid the obvious fact. They were born in that country. Born there. It is their home.
Are you yearning to throw out of their country of birth any other people that you can think of?