After I've tried rebooting my machine and router, changing DNS and using this fix, I finally found a method that worked for me an a bunch of other friends as well.

Quoting it from Reddit:
Inside your \Program Files (x86)\Square Enix\Final Fantasy XIV - A Realm Reborn\boot is a .ver file called ffxivboot. Take that file and drag it onto your desktop, open it with notepad, there'll only be one string of numbers, change the last number from 1 to 0. Save the file, and drag it back into folder. Then run the ffxivboot.exe file as an admin, and your launcher should update.
I have the Steam version of the game, if that's the case for you as well the file location will be different, if you just type ffxivboot.ver in your machine search bar it should pop up pretty quickly. Just right click it and select "Open file location" to make sure you are moving it back to the right folder. Hope this helps!