From the Earth to The Moon

Could this be NASA's Next big move?

In short no. There is no way any person could survive the launch and return accelerations required to do this. Not to mention factoring in air resistance the shell would get so hot you could cook eggs on it, and would probably bake the brave astronauts before they made it to space.  Then actually launching the cannon would bee impossible. Even if the canon got funding and a mountain was alloted to be hallowed out the sound off it firing would shatter class, deafen those working on it and around it, and would destroy the wildlife and ecosystem around it.
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Did anyone actually try this?

Surprisingly Yes. The united department of defense attempted to build a space cannon called the HARP project.  Though it was not meant to send people to space they did want an inexpensive way of getting satellites and other things to space, and long range weaponry. These tests however turned out to be unsuccessful and the project was scraped.   Picture left is a 16 inch harp cannon test firing one of it's cartridges.