PlayStation 4's day-one patch can be downloaded from PlayStation.com and installed to the system via USB flash drive.
This option, an alternative to downloading and installing the update on your console, should help customers without stable or fast internet access at home, as the update could theoretically be downloaded at a friend's house, public library, or school. The update itself will be necessary to enable Blu-ray and DVD playback, but not the playback of offline games--you can boot up Killzone, Knack, or any other disc-based title and play PS4 for the first time while the update downloads in the background.
A third option is to call Sony Computer Entertainment Consumer Services at (800) 345-7669 to receive a Blu-ray activation disc in the mail.
Game patches in general can also be downloaded while you play the game in question or another title, but online multiplayer features would likely be disabled in the meantime. It's not entirely clear from the PS Blog FAQ, but it seems game and system updates cannot be installed while an application is open--you'll have to quit back to the menu for a few moments in the meantime.
For all things PlayStation 4, keep it here at PlayStation Universe.