There are several ways to show or hide the publication date of your blog posts:
For all blog posts at once (within a particular blog section)
NOTE: To edit the publication date, take a look here: Website builder: How to schedule a blog post
Show or hide the publication date of a particular blog post
1. Within the editor, open the blog management panel on the left. Find the blog post in question and click on it:

2. Click on the blog post's header section and open its settings:

3. In the Style tab, show or hide the Date published by clicking on the eye icon:

4. Finally, update your website.
Show or hide the publication dates of all blog posts at once (within a particular blog section)
1. Within the editor, find the blog section, click on it, and open its settings:

2. In the Style tab, show or hide the Date published by clicking on the eye icon:

3. Finally, update your website.