Well, the primordial objective is seemingly survival. You come into the world with impulses to survive, as does almost every other animal. as they have for millions of years. Though, I don't think there is a known equation for survival.

Is there a proof such that x can not be found without an equation? Don't know of any. Even though we might not be able to find survival within a mathematical equation, it is a fundamental and primordial feature of life.

You might also like to read some Schopenhauer, as his views of the purpose of life may even go further than survival itself.

I came to the same conclusion about survival, but I did not consider it an "external" objective, "having been set prior to my own existence".

It is an imposed constant objective by my own nature.

To go back to the idea of an "external" objective, it is asking: "what should I do, were I immortal?"

I feel like once I have achieved the first internal goal of eternal survivance, there is nothing else to use this immortality for.

To the question "what should I do, were I immortal?"
my answer would be: "whatever you wish to do, you are immortal".

I have no background in mathematics, but the first step in turning a statement into a mathematical formula would be to express it as a deduction in formal logic.

That said, unless the premise is that the clues are indistinguishable from random physical events, would not the voice of God literally telling you what your purpose in life is constitute pretty solid evidence?