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At some point in the future, every stick figure will inevitably go back in time and become their past self, either by dying and respawning in the past or through some time travel power. So there's no point at which they "come to be".
For some, that's the whole story (ignoring Limbo): Go to future, die, respawn in past, repeat. As you might expect, that's not where it ends for everyone.
See, stick figures respawn at a random time and place, so they can die any number of times before ending up back where they started. And every moment they're chasing the trail left by themselves in the future in an endless ouroboros of fate.
Of course, they can't remember the immediate future. As time passes after an event (from their perspective), they forget details of the event. After half their lifetime has passed, the event is totally forgotten. So if they live for a total of 80 years, they may or may not remember the past 40 years, but the 40 years before that (which is also the next 40 years) is guaranteed to be forgotten, and is marked in red on the diagram.