In the modern age? Cells beget cells, and proteins for DNA management are transferred during cell division.
If you’re asking about evolution going further back, RNA can form structures that act like enzymes (an example: ribosomes, which make proteins, have enzymatically active RNA structure). It is hypothesized that early life used RNA for information storage and for structure/enzymatic activity.
DNA is more stable than RNA, so, the logic of this hypothesis is there was eventually evolutionary selection for organisms which formed DNA as their primary information storage. Similarly, proteins can be more stable than RNA.
It should be noted that this is a pretty active area of research, so our understanding of this topic is also regularly being updated.
This is a very simplified answer since this is ELI5!
Your question is about a much bigger concept. It also doesn’t have an answer. It is similar to which came first the chicken or the first egg.
Your assumption about enzymes might be incorrect but how an organism of human complexity arise is the same question but on a much more complex scale and the answer is, we can’t tell you.
The place where science and religion have their own domains shown by this question.
Science answer questions about the physical world but cannot always provide the desired answer. Science is pretty accomplished at how but not as well as why.
Religion is really good at why and not good at how.
DNA is a stable form of RNA. Both carrying genetic code. However plenty of RNA molecules are themselves enzymatically active. So the most likely explanation is at some point a piece of RNA randomly formed, that had the ability to copy RNA. From that point on you just need evolution. Since proteins are much more stable than RNA, any time rna came about that could create protein from reading an rna template rather than new rna, it would propagate. Enzymes don’t have to be different to rna. Enzyme just refers to a property of a molecule to catalyse some chemical reactions. In modern life forms most enzymes happen to be proteins, i.e. made from amino acids. But RNA just refers to the chemical structure of a molecule. So it can be inert or it can itself be enzymatically active. As for how life came to be: cell membranes are easy. Those happen any time you put a bit of soap in water. The individual soap molecules align to keep their lipophilic parts together and the hydrophilic parts to the water. Cell membranes are no different. They are just heavily stabilised fatty acid bilayera. Over hundreds of millions of years the living cells that preclude all our modern live evolved to put specificity modified fatty acids and peptides into their cell membranes to make them more stable. But in a mild environment, a pure phospholipid bilayer cell membrane is perfectly stable. So you end up with some small pond containing the individual rna building blocks and the lipids for cells. Randomly arranged rna ends up in such a lipid bilayer membrane and starts producing more of itself. And by random chance we eventually end up with modern cells.
Basically this step only had to happen once millions of years ago.
From then on it was a continuous cycle of RNA/DNA being read by enzymes making more enzymes which in turn replicated the DNA/RNA.
So what you’re looking for is called “Abiogenesis”, or how life arose out of non-living stuff.
Basically, if you take the right mix of elements in the right conditions, they will naturally start to form amino acids.
This is step one.
Over a long enough time, the amino acids react and you start to see nucleotides form, and nucleotides then bunch up to form RNA and eventually DNA (and all the other stuff needed for life)
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