Setup wordpress as subpath but in different root

Main site: example.com in /var/www/example.com.

Wordpress blog: example.com/blog in /var/www/blog.

Can't make it work.

server {
    listen 80;

    server_name example.com;

    root /var/www/example.com;

    # Add index.php to the list if you are using PHP
    index Index.html index.html index.htm index.nginx-debian.html;

    location ~* \.(ico|jpg|jpeg|png|gif|swf|css|json|txt|sd|html)$ {
            try_files $uri =404;
            access_log off;
            expires 1d;
    }

    location ~* \.(js)$ {
        gzip_static on;
        gunzip on;
        try_files $uri =404;
        access_log off;
        expires 1d;
    }


    location /blog {
        alias  /var/www/blog/;
        #try_files $uri $uri/ /index.php?q=$request_uri;
        try_files $uri $uri/ @blog;

        location ~ \.php$ {
            fastcgi_split_path_info ^(.*\.php)(.*)$;
            try_files $uri =404;
            include       /etc/nginx/fastcgi_params;
            fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
            fastcgi_param PATH_INFO $fastcgi_path_info;
            fastcgi_param PATH_TRANSLATED $document_root$fastcgi_path_info;
            fastcgi_pass unix:/run/php/php7.4-fpm.sock;
            #fastcgi_index index.php;

             #include the fastcgi_param setting
            include fastcgi_params;
        }
    }

    location @blog {
            rewrite ^/blog(.*) /blog/index.php?q=$1;
    }
}

For http://example.com/blog got 403 Forbidden. Looks like alias doesn't work with try_files.

But even http://example.com/blog/index.php doesn't work. Got File not found. .