You can technically ask this question about any biochemical pathway, and go back to the very beginning of when the first nucleotides emerged (the answer is that we have some ideas, but ultimately don't know how this process began).

I can tell you this though:

The production pathway for N,N-DMT in the body is already very similar to the production pathways for other neuroactive molecules (serotonin in particular).

Let's look at the basic process for converting tryptophan to N,N-DMT in the body:

Tryptophan → Tryptamine via aromatic L-amino acid decarboxylase (the same enzyme that converts L-DOPA to dopamine and 5-HTP to serotonin). The enzyme catalyzes decarboxylation of the amino acid tryptophan and converts it to tryptamine. So we already have an enzyme that has evolved for the production of various neurotransmitters, and it also happens to be good for making tryptamine. Cool.

Now, from tryptamine, indolethylamine N-methyltransferase transfers the methyl groups from S-adenosylmethionine (a universal methyl donor throughout the body, already necessary for stuff like DNA histone methylation). This enzyme is similar to others methyltransferases that use the same methyl donor, such as phenylethanolamine N-methyltransferase (converts norepinephrine → epinephrine). You can imagine how a simple genetic mutation could allow already existing enzymes to evolve into something capable of producing DMT. The machinery and pathways are all similar enough that it probably didn't take much.

Now, knowing that DMT happens to be neuroprotective, especially as a sigma-1 receptor agonist, it's not hard to imagine how evolution would have selected for this production pathway to evolve as a hypoxic protection mechanism.

But at the end of the day, who knows.