No.
Defences against CSRF depend on the page from which the request is sent and the server to which it is sent agreeing a unique identifier for the user.
Since the form is static, you can't place that unique identifier in the form.
If I have a script in the static site build the form on each page load with data requested from the server (cookie value, csrf token as well as field values etc) could that work?
Only if it is a server side script (so the form wouldn't be static), otherwise any site could include it to get the token.
I noticed the PHP Slim Framework's CSRF middleware only protects from POST, PUT & DELETE methods, not GET.
This is because GET requests shouldn't be doing anything in the first place, so (unless you are abusing them) there is no need to apply CSRF protection to them.
In particular, the convention has been established that the GET and HEAD methods SHOULD NOT have the significance of taking an action other than retrieval. These methods ought to be considered "safe". This allows user agents to represent other methods, such as POST, PUT and DELETE, in a special way, so that the user is made aware of the fact that a possibly unsafe action is being requested.