How can I have Finder doesn't sort strictly by the time metadata and not the grouped filename?

See the following screenshot:

This are screenshots from the Chrome/Safari, on OSX 10.12.1.

Notice that this is clearly not in the right chronological order. The last screenshot was taken at 1:09 PM, but it is neither at the top nor at the beginning of the list. This is frustrating, because this forces me to visually search when I want to send a screenshot I just took to a friend.

Is there any way to change my settings so Finder sorts by date?

The toolbar specifies how to group the files and clicking the column name is for sorting the files. If you want to reorder the files, just click the column name directly.

Based on your screenshot, you're grouping by "Date Created" and then sorting by "Name". You can see the group names are "September", "August", etc.

You can fix this: set the grouping (using the toolbar) to "None" and then click on the "Date Created" column name, that should fix your issue.

EDIT: If you're not using the List view, you can press ⌘J to open "View options", then click the drop-down there to Sort by "Date Created". I know it's annoying, but that's how it is.