I inherited a site that didn't use a child theme, and now it needs to be updated. Can I take the original parent theme, change the style sheet header, copy it into the root, delete everything but wp-content and make it be the child theme? In the past, I've loaded any files I wanted from the parent into the child theme, and it is my understanding that the browser will prefer whatever's in the child theme.
That is 100% the approach you should take. You can even set up the child theme with a folder
your-child-theme-name/ and then a style.css which uses the parent as the template:
Then, you can either import the styles into this style.css (
@import url('../parent-theme-folder/style.css')) or start from scratch as needed.
You'll also be able to pull in files you want to edit (like header.php or footer.php).