Probably not. The last universal common ancestor (LUCA) of all life, circa 3.6 billion years ago, was bacteria-like and most likely to be free living (or somewhat colony forming). It's unlikely that a free living organism could have a genome as small as 438 genes. We also know that most major protein structural families data back to that period so a fairly complete repertoire of possible biochemical functions would have been within evolutionary reach to the LUCA. So it seems likely the LUCA was quite sophisticated from a biochemical function POV. We see that contemporary bacterial genomes tend to favour minimum levels of redundancy but that isn't the same as having smaller numbers of genes. Different types of bacterial genomes have very diverse counts of the number of genes present. Between these observations there's little reason to suspect that the LUCA's genome was minimal.

Anything older than the LUCA, such as pro-genotes (things before "modern" genomes appeared) or even earlier forms would have been substantially different to an organism with an organised genome of 438 genes. The further back in time you go towards the abiotic origin of life the more "weird" and less cellular early life probably was. There remains a reasonable chance that the earliest self replicating systems were just soups of nucleotide chains, which would arguably be the earliest life-like things on earth (circa 4.6 bya), and that's quite unlike a genome-containing cellular organism.

It remains a very open question what the earliest self-replicators that gave rise to cells might have been but all the options are pretty weird. Here's a somewhat decent summary of some models

https://www.bionity.com/en/encyclopedia/Origin_of_life.html