The chicken-and-egg problem can take a certain amount of effort to solve, but it's not a major engineering obstacle.

The easiest way to bootstrap a self-compiling compiler from bare metal is probably by writing a Forth inner interpreter in machine code, which is a few hundred bytes; a Forth outer interpreter in threaded code, which is a few hundred cells; and then an interpreter for the language of your compiler in Forth, which is likely to be a few dozen to a few thousand lines of code, depending on the language. (I don't know if Forth is good for anything else, but it's optimal for this.)

I don't know how to estimate this task properly, but I doubt it's more than a few weeks of work for a skilled person.

But the claim wasn't that having the genome is directly useful, rather that it's a decent approximation of the upper bound on the irreducible complexity.