EBT is relevant. If we're providing for the child's basic needs already, that frees up more money for spending on whatever the parents want if the child tax credit is increased.
I just find it really strange to specifically target this set of people when there would still be a large underclass of people who don't share in the transfers. See these two graphs, for example. The economy has been really bad for a lot of 20-somethings. A lot of people wouldn't be able to get relief at all.
For the US, this already isn't a problem. Nothing like Japan. And sometimes it's necessary as was the case with China. But we could and should take more immigrants. It's more efficient than trying to modestly increase birth rates here.