The incorrect assumption here is that disbelief is an active state. Denouncment and denial may be active states of thought, but disbelief is a passive state. Like the way that on and off are an active and passive state, respectively. The argument that disbelief implies the denial of something that therefore must exist to be denied at all is inherently flawed by this assumption. If I, being in a state of ignorance of subject "x", would have neither belief nor disbelief in "x", but total unawareness of "x"s potential existence as a subject. To then be told by an outside perspective that "x" exists and I must believe in that existence without any proof of the claimed state of "x", I could choose to continue without further consideration of "x" and my existence would continue without belief or disbelief in "x", only knowledge of that concept existing for outside perspectives. However, I could more easily explain this reasoning to others with the simple statement "I do not believe in "x"." My statement would be reductive and simplistic, yes, but would do nothing to prove that "x" must exist and hold my belief because I have any knowledge of its concept.
The claim must be proven by the one making it, not the one being told of it.
This is great!