Do you mean the initial installation? I wasn't aware that it would try to download updates during initial installation, but if that's the case, make sure you're offline. Not just signed out of PSN, but completely disconnect your PS4 from the internet. Unplug your ethernet cable, if you're using a hardline connection, turn your WiFi off, if you're using WiFi. This way, it installs the game without any updates, then you should be able to update afterward without any issue.
If the game is installed and the updates are downloaded, but not installing, your only option is to uninstall the updates (only the updates, not the whole game) and start over.