Hi Satarra-
Thanks for reaching out! I’m sorry to hear about the issues with your blog page.
Even after deleting your fist Latest Posts page, you should still be able to set the new one. There are two places to do this- in the Customizer as you mentioned, as well as the Settings > Blog menu.
From what you’ve described seeing the “Nothing found” message, it sounds like you may need to make sure that you have at least one Blog Post to show on the blog page. Look for the Posts > Add New menu to add a new post.