Again, it just takes an engineer. Material tolerances, etc are all well established and publicly known scientific certainties.
Orbital mechanics are really not all that difficult if you're "better than High School" at math.
There's even publicly available simulators for this exact thing. The issue with ICBM's is the technology of getting them up high enough and in the right spot, you need very very little course correction once you hit apoapsis and begin coming down again.
Private companies do this, it's literally just math, you can even extremely accurately calculate the exact fuel requirements.