By chance?

[Mister Agenda]

It's not remarkable that all the requirements of an existent creature are met, when we observe that the creature does, in fact, exist.

You forget it’s “unremarkable” that even the simplest of proteins to even come into existence  is so improbable that it’s deemed impossible. Quite cavalier of you to dismiss the requirements for a creature, one after another, like marbles in a bowl coming to a very certain rest at the bottom center.
It fits your narrative to base your existence on sheer luck of mutations

When you're talking about the 'simplest proteins arising by chance' you're talking about abiogenesis, not evolution. At any rate, no matter how the first protein formed, proteins are amino acid chains, amino acids naturally link into protein polymers, so simple proteins would have formed spontaneously in the conditions believed to have existed in the Hadean era. It's relatively simple organic chemistry (or at least relatively easy to synthesize), which existed before life did. Again, there were simple protein molecules before the first cell.