The ‘edit’ button will appear next to the post title (or nearby) if you are logged in and have ‘edit’ capabilities. The placement of the button (or link) is dependent on the theme. Some themes don’t display it next to the title. But you do have to be logged in to see it.
If you are logged in, you should also see the admin bar (black bar) at the top of every page. So, that’s another way to edit a page/post from the front end. But you do have to be logged in, and your user has to have ‘edit’ capability.
So I would log into the back end (assuming you can and are allowed), and see if the black admin bar shows up. Then go to the front end (public side) of the site – in a different tab, if you wish – and see if the edit button/link appears. If not, then your theme doesn’t show it – you will have to modify the theme (use a Child Theme, of course).