What is the highest threshold speed of a space rocket traveling in an air pressure of 14psi with all of its stages if they where able to leave a solo at Mach 1 or more?
Probably the historical highest was the Sprint missile which accelerated at 100 G and hit Mach 10 in 5 seconds, amazing speeds in the atmosphere. Obviously it had severe thermal issues. It was also a silo-launched popup missile which lit off after it left the silo.
In the video you can see the characteristic very low speed of the missile at which the engine ignites after emerging from the silo. It is hard to imagine that if there were a practical means of accelerating the missile out of the silo, it wouldn't have been done for this application. (Sprint's mission was to intercept incoming nuclear warheads that had made it through a higher altitude interception screen - it was all about getting to the target quickly)