I tend to think you're right that "God" (in the general sense) is not falsifiable.

But, as a Christian, and someone who studies the Bible daily, I can say that at the very least, the God of the Bible is falsifiable.

For instance, if you could prove any one of the following statements to be true, the Christian message would fall apart (and indeed, some of these are even called out in the Bible as essential to its message). If you want a roadmap to debate Christians, here you go:

    - Jesus Christ never existed as a real human being.
    - Jesus wasn't "sinless" (according to the Biblical 
      definitions of sin).
    - There exists at least one other person than Jesus who 
      has never sinned.
    - Jesus wasn't crucified by Roman soldiers at the behest 
      of Jewish religious leaders.
    - The resurrection of Jesus didn't happen.
    - Jesus' mother wasn't a virgin.
    - Jesus never actually claimed to be God.

Many falsifiable propositions are made in the Old Testament, too. These may apply to Judaism as well, though I claim no particular expertise in that religion other than where it overlaps Christianity. Proving these propositions false would go a long way to discrediting the God of both the Old and the New Testaments:

    - The Genesis account of creation.
    - The Genesis account of a great flood.
    - The Genesis account of the destruction of Sodom and 
      Gomorrah.
    - That Joseph interpreted a Pharoah's dream and became 
      second-in-command of Egypt.
    - That Egypt never had a 7-year famine which they 
      survived because of storehouses of grain.
    - That Egypt never enslaved Israel.
    - That the plagues mentioned in Exodus never befell the 
      Egyptians (notably the plague of the firstborn).
    - That Israel didn't walk across the Red Sea.
    - That the Egyptian army wasn't drowned in the Red Sea 
      in pursuit of Israel.
    - That Samson never existed.
    - That Esther never existed.
    - That Esther wasn't a queen who saved Israel from 
      genocidal annihilation.
    - That Ruth never existed.
    - That Jonah never existed.
    - That Jonah never preached in Nineveh.
    - That Jonah was never swallowed by a whale/fish.
    - That Daniel didn't serve in the court of the 
      Babylonian/Medo-Persian empires.
    - That Daniel didn't accurately predict hundreds of 
      years of political wars and intrigue in the Ancient 
      Near East before it happened [0].

There's lots more than that, of course, but it's a start. In short, Christians believe in taking the Bible at face value. There are hundreds, if not thousands, of claims which the Bible makes which are definitely falsifiable. Claims of particular events happening to particular people living in particular places at particular times. There's nothing stopping you or anyone from falsifying those claims.

Not to do your job for you, but consider that there are several ways to do this:

    - Discredit the Biblical story's internal consistency.
    - Find contradictory archaeological evidence.
    - Find contradictory, reputable historical accounts.
    - Come up with valid textual criticisms.

... and I don't believe that's even an exhaustive list.

Good luck and Godspeed! ;-)

[0]: https://www.christiancourier.com/articles/869-amazing-prophe...