Can science prove that it is impossible for God to exist?
The god of the Christian Bible can be ruled out with just reason and a Bible by virtue of being ascribed mutually incompatible features rendering it logically impossible.
But gods in the generic sense cannot be. Nor need they be:
- "Extraordinary claims require extraordinary evidence" - Carl Sagan
- "What can be asserted without evidence can also be dismissed without evidence." - Christopher Hitchens
Gods can be treated like any other creature that has been claimed to exist but for which no evidence has been provided.
We simply don't need proof that there are no gods. Nor that there are no vampires. We're also not waiting for proof of the nonexistence of brownies, elves, pixies, sprites, fairies, nymphs, satyrs, fawns, changelings, ghosts, goblins, spirits, giants, doppelgangers, demons, devils, angels, gods, djinns, succubi, incubi, zombies, mummies, werewolves, banshees, gnomes, trolls, imps, gorgons, gargoyles, dragons, mermaids, unicorns, sea serpents, furies, harpies, fates, muses, graces, minotaurs, medusae, gremlins, warlocks, sirens, angels, phantasms, poltergeists, specters, zombies, djinns, spooks, demons, wraiths, revenants, phantoms, ghouls, apparitions, or eidolons.
They're all on the same shelf with the cyclops, the White Walkers, and the Kraken. We’re free to ignore them all without evidence or counterargument.