I don't think a government-provided baby sitter would be such a bad thing. If we made that baby sitting time educationally enriching, it might even pay for itself, long-term. Sure, some of those using it wouldn't be working people, they'd just be lazy. But having those kids spend a little more time outside of a lazy-parent setting and in an enriching educational one would presumably be good for society, when they grow up to be more productive adults.
If you really dislike that idea, though, there would be ways to do the daycare that require proving eligibility by showing evidence that a person is working, or actively interviewing, or attending classes, or getting some sort of medical treatment or something of that sort requiring the use of daycare.
As for the debt level, I think we could get it under control with two steps:
(1) Reduce military spending to less insane levels. A normal level of military spending is between 1% and 2.2% of GDP. Pretty much every other advanced nation is in that range -- the UK's at 2.2%, France 2.1%, Germany 1.4%, Canada 1.4%, Japan 1.0%, etc. Let's say we still want to have far and away the best-funded military, so we shoot just above the top of that range, and have a $480 billion budget. That would still be almost double China and Russia combined. Yet it would save us over a quarter of a trillion dollars every year.
(2) Hike taxes to more normal levels. A normal tax level as a share of GDP, for an economically developed nation, is around 35% (that's approximately the OECD average once you take the US out of the mix). Yet ours is just 24.5%. So, hike our taxes just to the level where it's normal -- roughly half-way between Japan and Germany, at 35% of GDP, and that's additional revenues of 10.5% of GDP, or $2.387 trillion.
Between those two measures, we'd shift about $2.6 trillion towards the black. That doesn't quite get us to a balanced budget, relative to the current stimulus-heavy spending, since we're on schedule for about a $3 trillion deficit this year. But pre-COVID-stimulus, the deficit was always below $1.5 trillion, even at the peak of stimulus following the 2008 meltdown, so it would be enough to throw us into surpluses most every year, with plenty of room to spare, and then we'd go back to growing out of the debt, the way we did before the Reagan/Bush/Trump upper-class tax cuts and military spending surges.