Trebuchets don't mix well with space travel.
Rockets are required because the energy that would need to be fed into this super advanced "trebuchet" would essentially be a massive explosion. Destroying not only machine itself, but also the cargo.
In other words: Rockets slowly use up their fuel by bringing it along with them in order to not have to use a single ground-based detonation that would blow everything up.
There is a solution to all this however: Lasers. By focusing a high intensity laser emmitedemitted from the surface onto sails attached to whatever you want to send you can push it along without needing to use rockets. NasaNASA is already developing this technology today.