First of all, some of the vaccines are with DNA, not mRNA, and then there are enzymes like reverse transcriptase. Can you 100% rule out that by chance you are not e.g. infected by another virus (e.g. Hep B) that has loaded a copy of reverse transcriptase in your cells?
I know, it is a theoretical risk only, but not zero.
RE: My experience taking the first dose of the COVID-19 vaccine (Pfizer) Day 1