But in a way you're correct. That kind of proof would require induction from evidence. And no amount of empirical evidence is sufficient to prove moral necessity. So it would literally either take forever to prove that life is the ultimate value, or we would have to make do with limited evidence.
It's my observation that Rand only had faith in what she believed in, and waited for someone else to come along and do the hard work of providing some kind of evidence.
Choosing life, which you mentioned, also does not prove that life is the ultimate value. It only shows that someone chose an ultimate value. Death would certainly be an odd ultimate value, but in fact it can be such. It may be a dead-end, but it can serve as an ultimate value merely by choosing it. You may say that "death" makes all other valuation impossible. That's not true, as the case is that one only has to seek those values that make the value of death possible.