Rockstar has squashed at least one major bug preventing PS3 players from accessing GTA Online, but many issues remain between the ambitious multiplayer mode and mass playability. As such, it has shut down microtransaction options for purchasing cash packs.
An update posted to Rockstar Games' support page yesterday stated that a PSN server issue was unintentionally limiting the number of players who could access the game outright. With that issue solved, you can at least try your luck at joining the game and making it into the first tutorial mission.
Speaking of that troublesome tutorial mission, Rockstar's support page has a few stopgap measures to try while they sort things out: if you're one of the many who gets stuck in an endless loop of "waiting for players," try deleting and re-downloading GTA 5's most recent title update, deleting your current character and creating a new one, or try entering GTAO in Solo mode.
Some players have reported getting into the first race mission after waiting for a while, so you may want to give it a rest for a while rather than trying over and over again.
To be fair, Rockstar did advise players to expect a bumpy first few weeks.