I'm also a newish dad. Our only car is a Honda Fit and we're doing fine, I don't recall ever running out of space. I'm not sure what we'd need a SUV for as long as we don't go off-road.
Of course that'll change if we have a second child, but even then a minivan seems much more practical than a SUV.
A Honda Fit is like a Tardis - it seems larger on the inside than the outside and you can fit in an insane amount of stuff due to the flat floor plan. I used to own one (a Honda Jazz) and used it to shift fridges and other items you'd normally need a ute for.
Super reliable as well.
Of course that'll change if we have a second child, but even then a minivan seems much more practical than a SUV.