Congratulations OP!
Somewhat pedantic but worth highlighting the difference between “infertility” and “sterility.” The former can be temporary, the latter is permanent. A woman taking a birth control pill is infertile (unless, y’know, she lies and doesn’t take it), but not sterile, unless she was actually sterile to begin with.
The WHO has taken an interest in testosterone as a potential population control mechanism in the developing world, so the research here is actually pretty decent. It shows that testosterone is pretty effective in suppressing spermatogenesis (especially so in the presence of a progestin), and that many (perhaps most) men become practically infertile (i.e. sperm concentrations too low to conceive) within a year of starting TRT. At the same time, research also shows that sperm concentrations generally return to baseline given a long enough time horizon after cessation.
YMMV of course, and I wouldn’t recommend relying on it as a birth control method, but generally agree with the OP that sterility is not something to worry about.