The reason I would advocate for humans in general to keep procreating even if life sucked for everyone right now is the same reason I advocate that individuals having hard times don't just kill themselves and end the suffering now: because it can get better. I have hopes that humanity can create a future world that is not so full of suffering as this one always has been, and in order for that to be worth doing, someone needs to be alive in the future in order to enjoy it. — Pfhorrest
But I, an antinatalist, am not arguing that life sucks. Antinatalism does not entail pro-mortalism (that is, the view that we have overall reason to kill ourselves). Antinatalists are against beginning lives; they are not thereby against continuing lives that are already underway.
For an analogy: someone who discovers that, were they to get pregnant, their child would suffer some sort of disability and decides on that basis not to have a child is not thereby expressing a judgement that those with disabilities do not have lives worth living.
And the problem of evil does not assume that life sucks either, only that the evils of life are unjustified.
If some kind of simple utilitarianism is the correct normative ethical theory, then the balances of pleasures and pains in a life would settle the matter of whether it is morally right to bring it into existence.
There would still be a problem of evil even assuming that kind of view is true, and it would still have some very odd implications in respect of procreation (it'd imply we ought to start breeding like rabbits if, that is, most lives record greater average balances of happiness over misery). But the point is that to show God to be justified in creating innocent sentient life one would only need to show that the pains were necessary to secure some maximal quantity of pleasure later.
But utilitarianism is false and certainly I am not assuming it is true and most of those who believe there is a problem of evil do not assume it is true either. Happiness is not all that matters. Dignity matters and it matters what kind of person you are. Better, for instance, to be a miserable kind person than a happy bastard. Better if wicked people suffer than good people. And so on.
For example, imagine two possible worlds. One is full of good people who are miserable. The other is full of wicked people who are happy. Which is the better one to create if creating one and one alone is the only option you have? Which one would a good god create? Surely it is not obvious.
But, importantly, if the god also had the option of creating neither, then surely the god would take that option?
Or imagine that only way to make everyone else maximally happy is to make one person utterly miserable. Would a good god create such a world? Surely not. For that world, though it contains maximum happiness, also contains a terrible injustice. And a good god would resist creating a world that contains an injustice like that.
In saying that am I thereby committed to the view that, if we live in such a world, our lives are not worth living? No, clearly not. Most of the lives in that world are most certainly worth living. Eminently so. Yet I think no good, omnipotent, omniscient being would create such a place.
And if we lived in such a world - that is, a world in which we are all happy bar one person whose miserable life is a necessary condition of our lives being happy - then though we have no obligation to kill ourselves we would, I think, have an obligation not to perpetuate the situation by breeding (assuming, that is, that breeding perpetuates it).
My point, then, is absolutely not that most of our lives are not worth living. I think most of our lives are worth living. My point is that it is reasonable to believe that an omnipotent, omniscient, morally good god would not create a world like this one and that, on that basis alone, it is reasonable to infer that we would not be good if we acted in a like manner and created more innocent sentient life and made it live here.