user17889: 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?

user19415: In the ultimate Truth there's no birth, past , present and future. birth is illusion.
That is why the Buddha said there is no apparent beginning. As there's no beginning for the rat horn or a sky flowers.

user471: 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 & 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.

17889: <p>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?</p>
 19415: <p>In the ultimate Truth there's no birth, past , present and future. birth is illusion.
That is why the Buddha said there is no apparent beginning. As there's no beginning for the rat horn or a sky flowers.</p>
 471: <p>Most suttas in <a href="https://suttacentral.net/sn15" rel="nofollow noreferrer">SN 15</a> like <a href="https://suttacentral.net/sn15.1/en/sujato" rel="nofollow noreferrer">SN 15.1</a>, have the following ending:</p>
<blockquote>
<p>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.”</p>
</blockquote>
<p>From a different translation of the <a href="https://www.accesstoinsight.org/tipitaka/sn/sn15/sn15.003.than.html" rel="nofollow noreferrer">Tears Sutta</a>:</p>
<blockquote>
<p>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;</p>
</blockquote>
<p>Please also see <a href="https://buddhism.stackexchange.com/a/34116/471">this answer</a>.</p>
