Chosen Solution
My new MacBook Air is stuck at the welcome screen. What now?
I would try booting in Safe Mode (hold shift while booting) and see if you can get in. If this works, there is something that is launching that is stopping the system from booting. Therefore I would go into System Prefrences > Users and Groups > Your login > Login items and then disabling anything you don’t recognise. If this doesn’t work, try booting to recovery mode (cmnd + R). This should allow you to reinstall the OS. I would try not wiping the drive first as reinstalling can keep your current Apps and data. This could solve the problem. If you can’t boot to this recovery, you can try internet recovery which is basically the same thing but it loads everything over the internet. To do this, hold (cmnd+optn+R) when booting.