Christians: would you admit that the evidence you claim proves your god could be used to prove other gods?

The most common evidence that I hear you guys claim proves your god is the fact that there is a reality. You say, “Look around you! Is this not evidence of a creator?” The other evidence you use is answered prayers and people miraculously surviving terminal cancer because thousands of Christians prayed for them. Would you ever admit that at best, this ‘evidence’ might prove that some divine power might exist and intervene in our lives, but no way does it prove the specific god of the Judeo/Christian doctrine? I mean, if this is all the evidence you have, it could just as easily prove any god and any doctrine, right?