Of course God is unfalsifiable

God's existence cannot be proven false.  Since God is unfalsifiable by definition, being unfalsifiable is a property of God's existence.  Since the statement God is unfalsifiable and cannot be disproven is accepted and supported by scientists and Atheists alike, then Occam's Razor shows the simplest explanation to be valid, since a defined and logical statement with scientific and academic consensus is more likely to be true than an argument against it. 

Calculus cannot be proven to be false.  Calculus doesn't wait for some physical evidence to appear and disprove it since Calculus is already logically defined.  We can't prove Calculus exists as a physical thing, but we know Calculus is valid.  Calculus uses self supporting axioms based on the unfalsifiable laws of logic, where abstract theorems do not require physical testability to be valid.  There are many invalid proofs by amateurs who try to disprove Calculus based on a limited understanding of Calculus and a desire to prove Calculus wrong, yet it doesn't matter if you choose not to believe in Calculus or if you declare all of it invalid simply because you don't like it, as such arguments will not make mathematicians everywhere drop the study of Calculus because you don't think it has sound logic.  No matter how you argue, Calculus cannot be falsified. 

Replacing Calculus with God's existence shows the same properties and the same reasons why arguments against them do not work.  Something can be both logically valid and non-falsifiable.

Mathfag here.

Reality guides the progress of Mathematics, but the math itself has no basis in reality. Calculus is simply a consequence of the axioms; a collection of theorems that describes the behavior of a large class of problems. Calculus doesn't really "exist", it's just that functions on real numbers happen to have some very nice properties.

Crackpots attempting to falsify Calculus is to be expected; the standard way introductory Calculus is taught is nonsense. You have to wait until you take a course on Real Analysis to anything rigorous.

Also, Occam's Razor is a nice heuristic, but is invalid in a logical argument. In fact, attempting to argue for or against the existence of God is meaningless unless you make more precise definitions. This holds even more if you're trying to make a tenuous link with Mathematics.

>Something can be both logically valid and non-falsifiable.

You're right, it can be verifiable. But if it can't be proven or disproven from a set of axioms, then there exist models of those axioms where it is true, and models where it is false.

And of course, "logically valid" is distinct from "true", "provable", or "sound".