Cargo-cannon delivery system from Earth to Moon?

Say that America/NASA has developed a small city with around 100 or so inhabitants on the Moon.

Would a cannon or slingshot or trebuchet type machine be able to launch cargo out of Earth's orbit and have it reach the Moon for them to grapple it and reel it in?

My main question is if the prospect of delivering interplanetary cargo without a rocket is feasible, just by building some sort of aerodynamic shell and giving it enough force to exit Earth.

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Cargo-cannon delivery system from Earth to Moon?

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