It seems to me that the macOS Preview app's purpose is to edit existing images. I'm wondering if it's possible to create new images from scratch. For example, I would like to create an illustration with some paintbrushes. Instinctively I'm looking for File -> New Image, but it doesn't seem to exist in Preview. Please advise.
No it isn't possible to create new images with Preview, as it is just meant for doing basic edits on images.(see @SteveChambers' comment)
If you really want to use Preview and not another app, just find a white image of the size you want and open it in Preview to edit and draw on it.
Otherwise, you can use 3rd party software:
GIMP, a free and open-source image editor with many capabilities, including creating and drawing images(fun fact: the very first Google logo was created in this program)
Keynote, made by Apple as a presentation app, but can also be used for simple drawings
Pixelmator (paid), a user-friendly image editor with many drawing/painting capabilities
Acorn (paid), a user-friendly image editor with many drawing/painting capabilities