THEIST: The universe has a beginning.He then demands that you address all of the subtle mathematical points of this new theory before you can go on to make your case that the universe has a beginning. If you've ever experienced this, then there is a good chance that you've had an argumentum ad cabbala thrown at you. What makes the argumentum ad cabbala fundamentally fallacious is that it tries to overwhelm the opponent with esoteric knowledge all the while the person employing it has no obligation to show how this esoteric knowledge is even relevant to the topic at hand or even if it corresponds to reality!
ATHEIST: I don't know, even evangelical scientists like Don Page say that science is open on that question.
THEIST: So what about Lawrence Krauss who said that all the evidence points to the universe having a beginning?
ATHEIST: But X has a model here where there is no beginning! Here, have a look at this twenty page publication with esoteric quantum loop string theory showing that...
The choice of Kabbalah employed by the atheist is usually frontier mathematical physics, but it could in principle be anything, such as obscure heterodox Marxist writings by Gramsci if your opponent's forte lies in the humanities rather than the quantitative sciences.
A good example of an atheist trying to use argumentum ad cabbala is Sean Carroll in his debate with William Lane Craig. Carroll is a third-degree Rabbinical master in cosmology from the yeshiva known as the California Institute of Technology, so it was naturally trivial for him to pull no fewer than seventeen different models of supposed eternal universes. Right away, the number of models employed is a red flag: why did he need seventeen counterexamples when one is enough? However, the big reveal that shows that this was all a tremendous waste of time was near the end when Carroll confessed that his preferred model violated the second law of thermodynamics. In other words, his model was unphysical.
What allows the atheist to get away with the argumentum ad cabbala is that he's counting on your kindness to carry most of the footwork while he has to do nothing. Even if you did manage to compute twenty or so pages of Feynman path integrals showing that this theory has problems on points X, Y, and Z, all the atheist will learn is that he needed to look for a forty page paper. And then he'll do just that and give it to you and demand you to work on that one while he has a night in the town.
This analysis points toward a solution for how to resolve an argumentum ad cabbala: force the atheist to do the equal amount of work in explaining how the model fits the evidence and even if it corresponds with reality. Remind him that he needs to show that your model conclusively disproves one of your premises and that it's not good enough to put forward a speculative theory that may have nothing to do at all with reality. If he shuts up at that point, then you can be sure that he had no actual points.