Can I fly the quad without an FPV screen?
Of course you can, it's called flying LOS (Line of Sight) as opposed to FPV (First Person View).
In fact flying LOS is a better way to start learning to fly your first quad because you'll have greater situational awareness (being able to see the
surroundings and their relative positions to the quad, the quad's reactions to your control inputs, better gauging of your speed and height, etc, etc).
After you've become comfortable with your ability to control the quad LOS you can then make the transition to FPV flying more easily (and safely)
than if you'd been flying FPV from the start.
One thing to keep in mind when flying LOS that doesn't figure into "the picture" when flying FPV though is that directions are reversed when the quad
is approaching you, as compared to flying away from you. For example: the tree at the left of the field you avoided with stick input to the RIGHT when flying away from you will then require stick input to the LEFT as you approach yourself. It's easier if you mentally picture yourself as the pilot.
If you've ever driven or flown anything RC controlled this is already obvious to you, and even if you haven't it will soon become second nature.
LOS gets really interesting when flying RC planes (or 3D quads) inverted towards yourself ... lol ... up is down, down is up, right is left and left is right