Is it possible for Hugo to generate a list of all posts with a URL structure like this? I’d like to keep the existing URLs instead of redirecting to a new URL structure.
Yes, but you need to create a section (root folder) with the name all-posts. If this isn’t where you store your content, you have to create one dummy content file for that section to be created. You will then have to create a list template that lists all the content with a paginator.