The word "only" is appropriate here. If you have an ICBM it's still a challenge to get to orbit. If you have a rocket capable of getting to orbit you automatically have an ICBM. If you've got the power to get to orbit you've got the power for a ballistic trajectory.
Heat shields are not trivial but they're achievable with 1950s era technology. If you pay the mass penalty you can just use a big "dumb" ablative heat shield. With a bomb you don't need to build anything too sophisticated, it only needs to work once and you don't want it back.
With a rocket capable of getting a meaningful payload to LEO you've got the power to pay that mass penalty if the trajectory is ballistic.
None of this is "easy" but it comes along with developing orbital capabilities. This is why Sputnik's launch was such a big deal to defense planners. If the Soviet Union could get a little satellite into a stable LEO it could deliver a warhead to the continental US.
Well, sure, it's not that simple, but the main point here is that it's "easier" to hit any point on the surface of the Earth with a rocket than it is to get a payload into orbit.
Nothing is simple in aerospace, and I'm sure there are things I'm missing. But generally speaking, an orbital vehicle becomes suborbital when it doesn't have enough speed to not fall back to the Earth. There's re-entry to contend with, but that's a solvable issue. And then there's the payload, also solvable.