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.
8. https://en.wikipedia.org/wiki/Mass_driver