Headed by John Hunter, the SHARP gun had a 47 m long barrel firing projectiles with expanding hydrogen. The tests were designed as a precursor to the "Jules Verne Launcher" with a 3,500 m barrel length, that was designed in the early 1990s for first-stage satellite launch.
The concept of ballistic escape velocity is well proven. The largest challenge is maintaining such high velocities, because air resistance and aerothermal heating will significantly slow down any such object. It is claimed that a mineshaft cover for the Pascal-B underground nuclear test explosion on 27 August1957 reached escape velocity. However, it is very unlikely that the cover was massive enough (or shaped aerodynamically) to retain sufficient velocity to escape the earth after passing through the atmosphere. Escape or orbit requires leaving the atmosphere at high speed.