Rewrite laravel query parameters with nginx

I have a laravel web app that acts as a CMS and has several sites in one app. I access these sites with the following url:

my-site.com/site/1 - Leads to site 1

I want to rewrite NGINX so that i can point several top domains to their respective site in my CMS.

my-site-1.com -> my-site.com/site/1

How can this be achieved? All questions i can find wants to point a domain to a subfolder, i want to point it to a query parameter.

I use Larave forge + Digitalocean. This is my configuration file

# FORGE CONFIG (DOT NOT REMOVE!)
include forge-conf/default/before/*; #*/

server {
    listen 80 default_server;
    server_name default;
    root /home/forge/default/public;

    # FORGE SSL (DO NOT REMOVE!)
    # ssl_certificate;
    # ssl_certificate_key;

    ssl_protocols TLSv1 TLSv1.1 TLSv1.2;

    index index.html index.htm index.php;

    charset utf-8; 

    # FORGE CONFIG (DOT NOT REMOVE!)
    include forge-conf/default/server/*; #*/

    location / {
        try_files $uri $uri/ /index.php?$query_string;

        if ($http_host ~ "^(www.)?my-site-1.com$"){
          #I tried adding som conditional rules here
        }
    }

    location = /favicon.ico { access_log off; log_not_found off; }
    location = /robots.txt  { access_log off; log_not_found off; }

    access_log off;
    error_log  /var/log/nginx/default-error.log error;

    error_page 404 /index.php;

    location ~ .php$ {
        fastcgi_split_path_info ^(.+.php)(/.+)$;
        fastcgi_pass unix:/var/run/php/php7.0-fpm.sock;
        fastcgi_index index.php;
        include fastcgi_params;
    fastcgi_coect_timeout 18000;
        fastcgi_send_timeout 18000;
        fastcgi_read_timeout 18000;
    }

    location ~ /.ht {
        deny all;
    }
}

# FORGE CONFIG (DOT NOT REMOVE!)
include forge-conf/default/after/*; #*/