2007 Hyundai Azera is slow to start

Possibly a check valve in the fuel system is allowing the fuel pressure to bleed off completely once the engine is stopped. Try this, turn the key to ON and let the fuel pump prime the system (3 seconds). Turn the key back to OFF. Repeat this a few times and on the final prime, try to start it. If this works, further testing will need to be done to determine where the failure is.