That was quite a notion in Jules Vern"s day, even something proposed seriously by a few scientist.
May even be what sparked those human cannonballs at carnivals, some died doing that.
Just a few physics one would need to overcome.
First would be the acceleration impulse power to launch such projectile to escape velocity, the G forces would be massive( one can work the numbers) The rocket sleds of the 50s slowly accelerated at near 15 Gs, the limit a human can maintain consciousness, you are talking like 150,000 Gs. That would mash any biologic.
Now Jules Vern never did say how these people to the moon 'GOT BACK TO EARTH' so it would be a one way trip. Now to get a little more real hear.
The US navy has the most powerful 'cannon' on the planet. A 50 megawatt 'rail gun'. In a test, this gun shot a 7 pound projectile a distance just over 100 miles. the muzzle speed was 4800 MPH (mach 6+) or twice as fast as SR-71 blackbird, About as fast as the space shuttle reaching boundary on reentry, and we know how hot that got.
In theory, this rail gun 'might' be able to put a projectile into orbit for a while, but would not escape earths gravity.
With mans smarts, I suppose something like this is remotely possible, engineering a capsule that wouldn't burn up or disintegrate, a fluid atmosphere to take the G forces, a huge 'rail gun' design with tremendous power.
Just that there are far better methods for putting a human into space