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In your .htaccess you should be able to do something like what is shown by Chris Coyier on CSS Tricks.

Link to example by Chris Coyier: https://css-tricks.com/snippets/htaccess/subdirectories-redirect-query-string/

Since you don’t have .php in your URL, WordPress has most likely already created RewriteEngine rules for you to not need .php. But the result should still work fine.

EDIT:

Another example of this is shown with pretty much the same exact scenario as you.
It’s on Apache’s Wiki website: https://wiki.apache.org/httpd/RewriteQueryString
The example shown to do this in your .htaccess is something like this:

RewriteCond %{QUERY_STRING} ^(\w+)=(\w+)$
RewriteRule ^/path /path/%1/%2?