The Higgs Boson particle was theorized in 1964 but humanity lacked the technology to verify it's existence. It took scientists 49 years to develop the knowledge base that allowed for the verification of this particle. The existence of this particle was therefore un-falsifiable from the time is was theorized until the time when the technology was developed that allowed it to be verified and observed.
That's not what unfalsifiable means (and I suspect you know that). Even if we had no means or tools for getting for the Higgs Boson at the time, we knew what kind of tests could be done to disprove, or falsify it. Regardless of technological ability, everything in science can be proven wrong with the discovery of something that contradicts established theory. God is unfalsifiable, because there is nothing that we can discover that will disprove god. He could always be just out of reach, just like pink unicorns.
None of those questions s are interesting, BTW, since as of yet, none of them have any bearing on our lives or reality. One might as well ask "Do fairies shit in Avalon?"