So, I have done the following :
-Took off the Blu-Ray, uninstalled the game, deleted the game's data (was not an issue, as I wasn't able to play the game at all, didn't lose any sort of progress)
-Uninstalled the game
-Cleared the cache (switch off the PS4, AC Cord unplugged for more than 30 seconds etc.)
-Installed the game
-Installed the 1.05 update (make sure it downloads completely in once, don't pause or stop it during the process, you never know)
And it seems to be working. I can access the Podium Pass, got 10000 Pitcoins, and I played Time Trial for a bit.
Haven't tested other game modes like Career or MyTeam, will make an update if anything goes wrong.