If the game requires a higher OFW than the console is on you're in the same boat as many... left with a decision to make on waiting it out or jumping the Pirate ship and updating.
We've had several similar threads on this topic, and thus far the best advice I can offer is before getting a game check the PS4 Games Minimum Firmware Lists to find out its required version.
Gotcha, there are some work-arounds such as using a payload and these videos for 1.76 OFW to do it without signing into PSN but not for higher versions... yet.