But if you give people direct financial incentives to have more children, as OP wants, that's what they'll do.
Look what the birth rate was 200 years ago when children were considered retirement investments (or elsewhere in the world where that's still true).
In Australia, we have (had) the "baby bonus". Seems a bit wrong. I'd rather support sticks to things like childcare subsidies and so on. I have two children in childcare 3 days a week and it would cost me over AU$600/wk without the subsidies.
Obviously there has to be a strong balance between an incentive that keeps a reasonable birthrate and one that overly encourages those desperate for money to procreate. The latter is disastrous for countless reasons.
Not sure how they'd balance it with a UBI.
I don't think people should be jumping into parenthood without knowing what it really entails (costs and brutal demands on your time) so I'm sympathetic to your angle, but reality plays out differently. And kids are the result of some pretty basic urges that are obviously difficult for many to deal with appropriately (think ahead, get/use contraceptives, actually abstain, whatever).