Different install location

So I’m trying to download the Sonoma installer and getting an insufficient space alert, so I tried the following:

I have a rather small ssd drive (about 150gb) on my late 2011 MacBook Pro, I purged everything I could from it, deleted almost every application, every big file I could find, Time Machine isn’t on automatic backup so it’s empty and couldn’t get past 18gb of free space.

Now I do have an HDD drive that’s 500gb and it’s virtually empty, I literally have over 400gb and can’t for the life of me find a way or any sort of tutorial teaching a way of using it. Is it even an option? Is the SSD really the only place it could download the installer to?

I barely use this computer so I’m not very familiar with the intrincacies of its system, any help is greatly appreciated.