Is there something I can press on the keyboard to get Pycharm to auto-complete without my first having to type a letter?
The purpose of this is so I can see all the possibilities as opposed to only the ones that start with the letter that I typed, or if I don’t know what any of the possibilities are to begin with.
Example:

You can trigger different types of completion from the menu Code → Completion or using the corresponding keyboard shortcuts (depend on keymap):
Default completion shortcuts: