Ramjets were developed right after the second world war and Mach 4+ was reached in the fifites. It's complicated but not extremely. See Antonio Ferri or Lockheed X-7.

It turned out out solid fuel rockets are operationally more practical for the use cases like air defence, long range missiles that are ballistic instead of cruising in the atmosphere and so on. And jet engines are more efficient for subsonic cruise missiles. Ramjets are still used in some missiles like the long range mach 3 air-to-air Meteor.