The .env file is typically not included in your Git repo for reasons of security of your various credentials. You can define Environment Variables directly on your instance, or indeed define the production environment variables in Forge.
The vendor directory is a side effect of running composer install - based on either the composer.json or composer.lock files, it contains all of the dependencies that your app needs, and can be created whenever you deploy your project. A deploy script will comprise the commands necessary to (i) pull the code (if you are not using webhooks) and (ii) run any deployment commands including composer install and perhaps npm run production.
Just log into your Forge control panel. Select the server, select the site. Now on the left, there is an Environment tab. You can edit the .env there. If everything is the same as your dev environment, just copy/paste your env there (except changing APP_ENV=production, APP_DEBUG=false, etc)
