Firebase can be a good option for making a forum, especially if you are not comfortable with PHP. Firebase provides a real-time database and cloud functionalities, which can be very helpful for building a dynamic and responsive forum. You can also use the Firebase Authentication service to enable user authentication and authorization in your forum, which is essential for a secure and reliable user experience.
However, if you are already familiar with MySQL and Node.js, it might be a better option to stick with them. Node.js provides a lot of powerful features for building web applications, especially for real-time communication between the server and client. MySQL is also a robust and well-established database system with a lot of resources and community support available.
Why not use an existing forum software like Xenforo or Discourse? Both are really good options (although use PHP and MySQL). This forum uses XenForo.