I guess I'm speaking as someone who grew up driving in the era of smartphones and readily available GPS so even when I personally drive, I depend HEAVILY on Google maps. Like I'd really be lost without it.
I guess not relying on GPS map routing is something that I cannot fathom. It always impresses me when friends can just rattle off highway routes and directions.
You might be lost for a while. What would probably happen next is that you'd start to build a mental map of the relevant territory, augmenting personal experience with some kind of map, paper or digital. Then you'd start developing the habit of getting directions or studying a map before you went somewhere there was a gap in the knowledge in your head.
At least, that's how it worked for me when I moved from a city so small (and grid-based) that nobody I knew used any kind of nav aid at all... to Los Angeles. I'm a little hesitant to say it would certainly work this way for everyone, given that variety in people's backgrounds and brains. But I suspect navigating is something people are generally more wired for than not. Chances are, you could do it too.
I guess not relying on GPS map routing is something that I cannot fathom. It always impresses me when friends can just rattle off highway routes and directions.