How did the original mental event arise according to Dharmakīrti's argument for rebirth?

[This answer on Reddit](https://old.reddit.com/r/Buddhism/comments/12flgq9/what_are_some_arguments_for_reincarnation_from_a/jfgry4f/) gave a basic outline of [Dharmakīrti's argument for rebirth](https://en.wikipedia.org/wiki/Rebirth_(Buddhism)#Metaphysical_arguments) in the form of a syllogism: 1. Matter and consciousness are metaphysically different, their characteristics and nature are different 2. An effect must be of the same nature as its substantial cause 3. Thus consciousness cannot arise from or be produced by matter (1, 2) 4. Conclusion: Therefore, there must have a been a consciousness prior to any person's conception which causes the first moment of consciousness in this life For the sake of the question, let's assume that you accept this line of argumentation. The question then becomes, how did the first mental event arise according to this framework? Of course, there is the idea that many immaterial intellects exist in the transcendent realms some of which stretch beyond iterations of the universe and many eons, but at the same time, for there to be so many creatures on just this planet with consciousness would implicate that billions upon billions, if not more, immaterial entities survived the past iteration(s) and eons and made it to this one, and also never achieved enlightenment during that time, which seems highly implausible. Perhaps the Yogacara idea of the store-house consciousness must be of use here, but it would be difficult to prove, I'm not too sure. If anyone knows more about Dharmakīrti's thinking with regards to this, please share your knowledge.