Nukes.[1] Lasers. [2] (Doesn't work, yet.) Balloons.[3] (Floating megastructures in the upper atmosphere is hard.) Giant cannon. [4] (Downside - huge g-forces on payload.) Extra fun with angular momentum.[5] (Even higher g-forces.) Exotic materials[6], with novel failure modes.[7]
Humanity has not been idle when it comes to imagining alternate ways to get to orbit. But so far, the only one that works in practice is rockets.
1. https://en.wikipedia.org/wiki/Project_Orion_%28nuclear_propu...
2. https://en.wikipedia.org/wiki/Laser_propulsion
3. https://en.wikipedia.org/wiki/JP_Aerospace#Airship_to_Orbit_...
4. https://en.wikipedia.org/wiki/Space_gun
5. https://en.wikipedia.org/wiki/SpinLaunch
6. https://en.wikipedia.org/wiki/Space_elevator
7. https://www.gassend.net/publications/FateOfABrokenSpaceEleva...
Big magnets. [8]
8. https://en.wikipedia.org/wiki/Mass_driver