My question transverses several fields of biology, this is why I think it can't be addressed by biochemistry, genetics, evolutionary biology or origins of life research only?

I know there is extensive research into the taxonomy and evolution of protein domains and many connections are found out and are continuing to be found between numerous domains. However, as far as I can see new domains always arise from preexisting ones and I have seen no paper showing the developing of new protein domain from a random piece of DNA which just mutates a start codon and synthesizes a new protein with no apparent function. I know this is theoretically possible but has anyone seen any evidence it has happened in any form of life in any geological period of time?

My thinking is that if it hasn't, than, does it means all protein domains are a kind of "progeny" of a single domain that arose at onset of life as we know it (or may be even was the first lifeform on Earth) or am I missing something out here? I tried hard to find any paper in any field-be it protein biochemistry, molecular genetics, evolutionary biology or origins of life but I wasn't able to do it.

It seems very strange to me this hasn't been pointed out by now thinking it's a relatively very simple deduction and I thought someone somewhere should had done some research on that or even just plain stated the hypothesis. So, I'm asking either for a reference paper showing evidence for the evolution of de novo protein domain unknown by now from a random piece of DNA that somehow managed to turn into a gene or for a reference to a paper discussing the idea that all proteins originate from a common ancestor existing at the onset of life and even, possibly, a single domain as old as life itself?

P.S. Am I mislooking something or is this hypothesis something new for molecular biology-with all that effort gone into identifying relationships between protein domains I'm thinking it's very strange no one has hypothesized a single "mother" domain for all life. Are there some mechanisms that could generate novel domains from non-coding DNA I had overlooked when searching the journals and if there are to what field do then pertain to?