I'm reposting an old comment by myself, with some small introduction to make it more relevant:
In spite your idea is not impossible, it would be very improbable.
One trick is to look at the features that are common between eukaryotes and prokaryotes, and try to guess which one are inevitable and are common to any life form in the universe, and which ones are essentially random and each life form would get a different random election.
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Nobody is sure, but if you allow me to guess ...
Perhaps DNA and RNA are inevitable, or at least they are the easiest solution for they problem they solve. I guess even the same sugars and some nucleotides. The only variation on Earth is that some parts of the DNA are methylated, but it can be added and removed. There are some weird bases in the RNA for very special task, but my guess is that they will use the same main bases. I'd not be surprised if alien has DNA and RNA that is chemically identical to us (but in other order).
Even proteins are probably inevitable. Here there is more wiggling room. We use 20 amino acids, but there are like 5 more weird amino acids that are mostly modifications of usual amino acids and are made after the protein is formed. For example collagen uses a lot of proline that is a normal amino acid, and also hidroxyproline that is a modification of proline made during the creation of collagen https://en.wikipedia.org/wiki/Collagen#Synthesis I guess that the list of amino acids used by aliens will be slightly different. Perhaps between 15 and 25 instead of the 20 we use. Perhaps also some replacements. But perhaps the list has some special property we have not discovered yet. I don't expect a smoking gun here to determine if aliens are unrelated to us.
The most interesting part is the translation from DNA/mRNA to proteins https://en.wikipedia.org/wiki/Genetic_code It's a translation from the 64 combinations of 3 bases of DNA/RNA to amino acids. It's almost blocked, so there are 16 blocks with 4 options in each one. But some blocks have small changes. We know like 20 versions of the small changes. The 20 versions are very similar, they are not very different. So it's possible to make changes in this translation table. The most interesting part are the 16 blocks. As far as we know the elections it arbitrary, like a frozen random initial election that was inherited by all of living things on Earth.
So the first thing to check in an alien life is if they translate in the 16 blocks the same amino acid that we translate. I'd be very surprised if this is the case. My guess is that it's almost random, and any election is fine, and each independent alien life will have a very different initial random election.