Not even in the earliest variant of the primordial soup theory there was any supposition that it contained proteins.

About a half of the amino-acids that are contained in modern proteins can form in the absence of life, and it was supposed that the "soup" contained those ten amino-acids.

The original "soup" theory did not explain how you could get proteins from amino-acids. Proteins cannot form within a soup, because they can form only by extracting water from amino-acids, which cannot happen when they are inside water. (The living cells extract the water from substances like amino-acids, in order to make polymers by condensation, by using special dehydrating agents that are acid anhydrides; the most important classes of such acid anhydrides are either polyphosphoric acids like ATP or thioesters; such dehydrating agents cannot appear naturally in a "soup".)

A way to form proteins would be not in a soup, but on some rock where the water evaporates and leaves a residue of amino-acids that could condense into proteins, more precisely into peptides, in the absence of water. However not even this is good enough to explain the appearance of a self-reproducing system. Such a system can appear only in a place where amino-acids are synthesized continuously (like attached on the surface of minerals with catalytic properties), and not like in the theory of primordial soup where it was supposed that they could be synthesized in the atmosphere, by lightning and UV light, then they would fall in the sea, which could have never concentrated them sufficiently in a single place.

Also the mineral ions that could have existed in a primordial "soup" are not those that could have provided catalytic functions. In the beginning, the primordial ocean contained mostly potassium ions, and later also magnesium ions, because these are the most easily leeched from rocks. The primordial ocean had condensed from volcanic gases and initially it contained only volatile acids, like hydrogen chloride and carbonic acid. Then slowly it has dissolved the more soluble parts of the rocks, so that the dissolved ions, starting with potassium, have neutralized the acids, and then other less soluble ions have been leeched from rocks, until eventually the ocean water has reached the current composition of its salts, but this happened after a very long time, most likely long after the appearance of life.

It would be very unlikely for life to appear in an ocean with the current salt composition, because many of the ions present now in sea water would interfere with the biological chemical reactions. All the living cells that are inside sea water spend a considerable part of their energy with preventing undesirable ions, like sodium and calcium, from entering the cells. At the origin of life, such highly-efficient ion pumps could not have existed, so such harmful ions must have been not abundant in the ocean of that time. Therefore the probability for the appearance of life is much higher on a young planet with a young ocean and the probability decreases on an old planet, where chemical equilibrium is reached.

The primordial ocean acquired relatively soon a high concentration of Fe(II) ions, but those are not suitable as catalysts in the form of hydrated ions. All the ancient enzymes that use iron as catalyst use it in the form of iron-sulfur clusters, exactly like the iron that can be found in non-soluble iron sulfide minerals, so it can be presumed that the original catalysts were iron sulfide crystals alone, without the protein part that is now attached to the iron-sulfur cluster, in order to position it correctly inside the living cells.