Proof requires correct logic.
Though one may prove non-existence within special limitations, such as showing that a box does not contain certain items, one cannot prove universal or absolute non-existence.
However, “existence” may be proven and the proof must come from those who make the claims of existence.
Who is shifting the burden of proof? In the end, it does not matter. NO ONE has presented any testable evidence or proof for the existence of a deity, souls, heaven, spirits, demons, angels, hell, afterlife, fairies, leprechauns, astral traveling, telekinesis . . .