I've been doing so much research, but it seems like all the articles out there are either sending notifications from the console or sending a push notification to a single device.
All I want is to send a push notification using Firebase ON my client and not on the Console to everyone. Do I need a server? If so, what information do I need to retrieve from it?
If you simply want to send a downstream message, you don't really need a server. You can simply use Postman or cURL. Just specify the registration token(s)/topic you want to send your message payload to.
If you are aiming to send the downstream message from the client (Android app) itself, I would strongly advise not to. Quoting a portion of @FrankvanPuffelen's answer here:
It is to avoid exposing the key to unauthorized users, preventing exploitation.