There are two places where posts generally are displayed on a WP-powered site:
– In the Admin Area (e.g., the Posts screen)
– On the front-end (e.g., the home page)
So any user can view posts on the front-end, simply by visiting the site. Of course, this depends on the theme that you are using. Most themes display posts in places like the homepage, archives, single-post views, and so forth. But your theme may differ, so you would need to ask your theme provider for more information.
Then in the Admin Area, as mentioned you need to have sufficient role/capabilities (e.g., admin) in order to manage posts. So if you have admin-level role/caps, you can view all posts in the Admin Area under the Posts screen.
Also this seems relevant. With USP plugin, all submitted posts are treated by WP just like regular posts. So anywhere you find regular WP Posts, you also will find any submitted posts.
Also maybe useful. You can control the Post Status (e.g., Publish, Pending, Draft, et al) for all submitted posts. Visit the plugin settings and look for the “Post Status” option. That way you can choose the Post Status for submitted posts.