Our Number of births going into the past has to necasserily be finite not infinite.an infinite number of births without a first is logically infathomable.so why did we first incarnate?
Transmigration has no known beginning. No first point is found of sentient beings roaming and transmigrating, hindered by ignorance and fettered by craving. For such a long time you have undergone suffering, agony, and disaster, swelling the cemeteries. This is quite enough for you to become disillusioned, dispassionate, and freed regarding all conditions.”
From a different translation of the Tears Sutta:
From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. Long have you thus experienced stress, experienced pain, experienced loss, swelling the cemeteries — enough to become disenchanted with all fabricated things, enough to become dispassionate, enough to be released."
Please also see this answer.
In commentary, we born by avijjā. Avijjā arises by Kāmāsava, Bhavāsava, and Avijāsava. These 3 Āsavā originate Avijjā. It's non stop loop.
I can see only stronger and stronger unwholesome in the loop. And I don't think we can find the beginning.
Ignorant > Old and Death > Doing (Managing) > Old and Death > Nāma Rūpa Arise > Old and Death > Senses Arise > Old and Death > Meeting > Old and Death > Feeling > Old and Death > Remembering > Old and Death > Managing > Old and Death > Craving > Old and Death > Craving again and again > Old and Death > Doing (Managing) for New Nāma Rūpa Arise as in Memory > Old and Death > Born as Managed > Old and Death > Arising Old and Death > Arising Old and Death > Arising Old and Death > Unlimited.