When you have hidden the edit button, there's two easy ways to edit the page.
Using the shortcut
You can use the "E" shortcut to edit a page, even when the edit button is hidden!
See the Confluence Server shortcuts infographic for more information.
Disabling HideElements via the URL parameter
By adding the "hideelements=false" parameter to your URL you can temporarily disable HideElements.
This will make the edit button show up again.
Example URLs:
https://your-confluence.com/display/SPACE/Awesome+Page?hideelements=false
https://your-confluence.com/display/SPACE/Awesome+Page?foo=bar&hideelements=false
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