adding a button to the top

Sorry, this can not be done without editing the PHP code of the plugin.

Could you tell me what exactly I need to do? I understand in PHP

If I understand what you want to do, you can probably append you content to the TOC variable:

• https://github.com/shazahm1/Easy-Table-of-Contents/blob/2.0.17/easy-table-of-contents.php#L622