RNA polymerase is the name for a family of protein complexes that use DNA as a template to synthesize complementary RNA. There are eukaryotic and prokaryotic version of this complex, and different versions are recruited in our cells depending on what class of RNA is being made.

In any event, these are all genes, that are transcribed and translated like any other.

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https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6095464/#:~:text=The%20Escherichia%20coli%20RNA%20polymerase,ribonucleotide%20(rNTP)%20as%20substrate.

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https://www.ncbi.nlm.nih.gov/books/NBK545212/

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I'm going to take a guess and say you are wondering how new cells obtain RNA polymerases. If you're thinking about the problem of making RNA polymerase without RNA polymerase, don't worry. When cells split, they kind of divide stuff up between them like marital assets during a divorce. So, each new cell already has RNA polymerases available to make new polymerases. Similarly, after meiosis, gametes will have RNA polymerases from the parent cell.

https://www.nature.com/articles/s41580-019-0208-1

If that's not what you are wondering, then RNA polymerase is made just like any other protein complex. It starts by transcribing the DNA (done by an RNA polymerase) to mRNA. This is occurring in the nucleus. The mRNA then goes to a ribosome witch will attach complimentary tRNA to produce a peptide. The peptides of each RNA polymerase domain will then fold (probably with the help of some chaperone protein) and then somehow be joined together.

If you really want to twist your noodle, look up the RNA world hypothesis. The theory is that before there were proteins, RNA did all the work that proteins do. So, replication of nucleic acids was carried out by self-replicating RNA. So then the question is, where did individual ribonucleotides come from?

> When cells split, they kind of divide stuff up between them like marital assets during a divorce.

That was good.

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