You shouldn't have to mess with any of that. You will, however, need to make sure that you've properly configured the server.
To set up the server environment, make sure that you've got the necessary programs (PHP and its required extensions, composer, Apache/Nginx, etc.). You'll need to make sure that you've properly configured the .env file with the correct database credentials and other environment-specific information. You'll need to run composer install on the server to install all the required dependencies and, perhaps most relevant to what you're describing, configure the web server to point to the public folder as the root directory. Also make sure that the public folder has the correct file permissions.