MacBook Air shows black screen with arrow on startup

If your MacBook Air starts up to a black screen with only the mouse arrow visible, press and hold the power button for up to 10 seconds until the Mac turns off. 

Wait a few seconds, then turn it on again. Apple: If your Mac starts up to a blank screen

If the black screen and arrow return, try macOS Recovery. 

On an Apple-silicon Mac, hold the power button while starting it until “Loading startup options” or the Options icon appears, then choose Options >> Continue. 

On an Intel Mac, turn it on and immediately hold Command (⌘)-R until the Apple logo or spinning globe appears. Apple: How to start up from macOS Recovery

If Recovery opens, you can use Disk Utility >> First Aid to check the startup disk, then restart the Mac. 

Do not erase the disk.

You can also try Safe Mode. On Apple silicon, hold the power button until the startup options appear, select the startup volume, hold Shift, and choose Continue in Safe Mode. 

On an Intel Mac, start the Mac while holding Shift. Apple: Use Safe Mode on your Mac

If neither Recovery nor Safe Mode works, Apple Diagnostics can check for certain hardware problems. 

On Apple silicon, hold the power button until the startup options appear, then press Command-D. 

On an Intel Mac, start the Mac while holding D. Apple: How to use Apple Diagnostics to test your Mac

The visible arrow does not by itself identify the cause, so it would be premature to assume that the problem is the display, graphics hardware, startup disk, or macOS.