How can I view my (non-Photos) photos full screen, and in order?

I have a large number of high-resolution photos on my MacBook Pro, organized in folders and subfolders, that I took with a non-Apple camera and directly imported without ever involving the Mac App "Photos". I don't want to have to import these pictures (1000s, and 1000s of them) into Photos. However, I am stumped as how to best view them in FULL SCREEN format and in ORDER. I don't want to set up a slide show (because that dictates how long I can look at each photo when I really want to decide that for myself). So I am trying to use Preview in Full Screen mode. However, no matter whether I select all photos I want to see and drag them onto Preview, or whether I drag the enclosing folder onto Preview, the photos appear in more or less random order inside the Preview sidebar, and using arrow keys to step through them one at a time after choosing "Full Screen View" results in the same random order. Even if I open their enclosing folder in list view within the Mac Finder and sort them by, e.g., date or name, once I drag the folder to Preview, I'm back to random order. So, hence my question: Is there any other program/method to look at my photos in full screen view (with a dark border around each, not some background screen image), and step through them one by one in some pre-determined order (date or name)? Or can I coax Preview into doing that? (And if not why not?!!)