The posted-on date by default appears below the post. How can I move the posted-on date above the post and below the entry-header? I'm using a child theme of Twenty Sixteen. Because the post-on date is generated after the content, I don't believe a solution is possible with css.
Copy the file that renders the section of the site from the parent to your child theme, keeping the structure the same as the parent. Then make the code change in your child-theme copy and the theme will then use that file instead.
See here for more information on doing this: https://codex.wordpress.org/Child_Themes#Template_Files
To move the posted-on date above the post and below entry-header, copy the template-parts directory with only content.php and content-single.php from themes/twentysixteen/ into your child theme. In content.php, move
twentysixteen_entry_meta(); from the entry-footer div to just above the entry-content div. This will put the posted-on date above entry-content on all the posts. Do the same for content-single.php and that places the posted-on date above entry-content on single posts.