If the quantum fields that created the Bing Bang and our Universe are eternal and Bing Bangs will keep bursting forever (see
https://bitcointalk.org/index.php?topic=1432165.msg17423455#msg17423455), then, soon or later (very later), there will be a Universe exactly like ours, with an Earth exactly like this, with exactly the same history, up to everyone of us.
And, following the rule that says that everything possible will necessarily happen, we'll just need to wait enough time, this will keep happening forever.
We'll be mortals, but will keep borning again on other Universes and Earths exactly like ours.
But, probably, we'll have to wait for trillions of years between each "reincarnation".
And we won't ever remember that we lived before.
The another "We" will be us, since it will have to be an exact copy to be us. And we are just exact copies of ourselves, since our bodies (all its atoms) are changed more or less on one or two years (see
https://bitcointalk.org/index.php?topic=1432165.0).
It seems Modern Cosmology is saying "reincarnation" on an identical body can happen.
Of course, these are just theories. We have no evidence of a multiverse or that there are and will be forever new Big Bangs.
But the mere possibility that we are mortal, but eternal, has philosophical consequences.
If we are eternal, looking for meaning by trying to obtain symbolical immortality (by our deeds or kids/genes: see the OP) is less important.