No, there isn't. There's an ancestor population.
"This organism survived objectively better than any other organism of its time"
No, it did not survive. Being an ancestor is not survival. And this has nothing to do with "optimization" ... if evolution optimizes survival, then your "single common ancestor" predated optimization. You're just throwing concepts together to support a prior belief, but the facts don't work that way.
"I think it's possible to define survivability objectively using a little graph theory."
Maybe you should actually try it. Perhaps then you would notice that your notion of "optimized survivability" is about the future, but you're talking about graphs of the past.
Are you sure about that? Viruses too? (depends on your definition of "living" of course) To clarify: I don't know if there is or isn't, I just don't think anyone does.
BTW this organism is called LUCA. Read: https://en.wikipedia.org/wiki/Last_universal_common_ancestor