Or, alternatively, to have fewer kids, if they were planning (as many parents in the USA do) to provide financial support for college to those children.
How's that? Every BI plan I've heard floated around starts paying out when a person reaches 18 years of age (absolutely college age). So, as soon as a child goes to university, they get BI, and parents don't have to afford a single expense. Seems to alleviate the burden of having a child in that age range.
Most near-term UBI proposals (and all plausible ones) wouldn't pay all living expenses in most college communities + the costs of actually attending college, so the idea that having BI available to college-age recipients would alleviate all parental burdens of college-age offspring is, well, sheer fantasy.
There are countries where university tuition is free, and the state also pays student benefits to every student, which makes it financially possible to study without receiving money from your parents.
Those countries tend to have lower birth rates than USA.
For the rest? We need more trade schools today, and we are talking about something theoretical at least years away and probably decades, when we will hopefully be past the ancient university model of tremendous expense and most people are taking courses online or through trade schools at very little cost.
Tuition is due a few times a year (usually twice, but some systems are quarterly). If the student gets a BI every month, there should be no issue affording tuition, in addition to living expenses.
Tuition, fees, books, etc., together at many institutions are, annually, is near or even greater than the total amount of annual per-person UBI in many proposals I've seen.