Strong atheism is, in fact, a religious belief: claims of the non-existence of gods are no more falsifiable than claims of the existence of them, so in order to “know” there is no god one must have faith.
Um… Show evidence that a god exists. Poof, you have falsified the claim that no god exists. Pretty easy, actually.
Your inability to come up with a way to produce evidence doesn’t make the strong atheist’s stance unfalsifiable. Unfalsifiable isn’t “We can’t produce any evidence that would falsify the claim right now.” That would take us to an absurd definition of the word where any scientific theory that requires more advanced technology than we currently have is “unfalsifiable.” That’s not what the word means.
The difficulty in proving that God exists isn’t what makes theism unfalsifiable. You shouldn’t make any assumptions about what can or cannot be proven true at some point in the future. What makes it unfalsifiable is that there’s no rational way to prove that God doesn’t exist, not because of an inability to collect evidence, but because the logical framework constructed by religious claims forbids it. Strong atheism has forbade no such thing. There’s no equivalence here.