Front Page button to add new element in node
There are ways. Here is one:

You will have to programmatically add value to that entity reference field. Here is how you should do it Programmatically update an entity reference field (see the multiple values case)

To make your button work you will need to add a route with arguments (one argument of the content ID you are adding a current user into) see here https://www.drupal.org/docs/8/api/routing-system/using-parameters-in-routes

And in order to add a button you can just update/override a corresponding twig template to inject HTML code of a button there referring the path of the route above with the nid as a parameter.