There are several causes for such symptoms. The car starting involves 'air, electricity and fuel' along with others. Below is for the fuel related and in particular fuel pressure issue. Here are the steps to check if the fuel pump and/or fuel filter are the causes for such delayed starting problem.

1. In the morning, before starting the car
2. Turn the key to ON and wait for 5 seconds
3. Turn off the key
4. Repeat abbove 2 and 3 steps 5 times.
5. Start the engine and check if the car starts right immediately.

If above testing results show that the car starts immediately, then fuel pressure is the casue for the delayed issue. Changing fuel filter and/or fuel pump will likely resolve the delayed starting issues.

For more details, please have your mechanic fully test your car.