My view of Darwinian life on Earth is (if anything) darker than most radical anti-natalists (cf. What are your thoughts on anti-natalism?). So let's here focus on the purely technical question. Is the most effective way to minimise, prevent, and ultimately abolish suffering (1) human extinction via radical anti-natalism? Or (2) genetically reprogramming the biosphere?

Clearly, there is no gene "for" natalism or anti-natalism – any more than there is a gene "for" belief in God (cf. God gene - Wikipedia). But this isn't what the Argument From Selection Pressure against extinctionist anti-natalism claims. There are fitness-enhancing genes / allelic combinations that predispose to, e.g. religiosity, and hence natalism (cf. God's little rabbits: Religious people out-reproduce secular ones by a landslide).

Of course, not all religious traditions claim that we have a duty to "go forth and multiply". Yet compare the fate of celibate religious communities like the Shakers with the mass breeders (cf. Sister Frances Ann Carr, One of the Last Three Shakers, Dies at 89).

Selection pressure against anti-natalism is also far more direct. Before the advent of family planning, the question of whether a woman wished to have children was often academic. But “broodiness” (cf. Broodiness: The Need to Conceive) is a heritable trait under a high degree of genetic-biological control. Men as well as women are susceptible (cf. Falling in love makes men broody) – some studies have claimed to a similar degree (cf. Real men are just as broody as women). Other things being equal, the slightest genetic predisposition not to feel broody, or feel only weakly broody and hence more susceptible to anti-natalist ethics, will be strongly selected against. Thus today involuntary childlessness still causes terrible heartache. People will go to extraordinary lengths to have children (cf. Indian woman who had baby at 72 says she has no regrets - but being a mother is harder than she expected). If anything, the unfolding revolution in reproductive medicine means that selection pressure in favour of broodiness will intensify rather than slacken.

I say more on anti-natalism here:
What are the main differences between the anti-natalism/efilism community and the negative utilitarian/”suffering-focused ethics” wing of the effective altruism community?
and:
What are the arguments against antinatalism?
In short, I’d urge everyone not to bring more suffering into the world. Yet if you are determined to have children, then you can at least load the genetic dice in their favour. Strictly speaking, life and suffering aren’t synonymous. Post-Darwinian life will probably be wonderful.