Why did we first incarnate? 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?
Most suttas in SN 15 like SN 15.1, have the following ending:

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 &amp; 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.&quot;

Please also see this answer.