Is it possible to install built-essentials GCC and friends on CoreELEC

Yay, I’ve got a nifty small Hexacore AML S922X and ssh setup with a storage of > 200 GB.
So… how do I compile on that board?

Can I install it with a package or do I really need to cross compile it first and push over ssh?

You either use a docker container and install the tools you require or (more easy) use chroot and install e.g. a complete Ubuntu environment. Please see my script at GitHub - beta68/install_cevdrx11: Installs VDR and X11 including Ubuntu 20.04 within CoreElec environment as an example.