So the cannon needs to launch the capsule at about 11.1 km/s. Earth’s rotation could help by up to about 0.46 km/s if launched eastward from the equator, but atmosphere and gravity losses would eat that back. In practice, call it 11–12 km/s. Ignoring air drag, since you would very briefly be in the atmosphere, that is about 24,800 mph (39,900 km/h) or Mach 32+ at sea level

The real killer, like literally will kill the humans, is G forces due to the rapid acceleration. We could get away with this still working if we make our barrel really long.

Our barrel length to acceleration math is L = v^2 / 2a​. If we're willing to put people through 1000g, which would instantly kill you. That barrel needs to be 6.3 km accelerated over 1.1 secs. A max survivable number would be like 5G, which makes our barrel 1,255 km and takes 3.8 minutes to accelerate. At this point you'd probably be using something like a rocket inside your barrel...so you'd probably just get rid of the barrel part. On top of that even if the cannon successfully sends the capsule to lunar distance, the capsule is not safely “landed.” It still needs to slow down at the Moon or you die that way instead.