To start an airline in the US you need two things. First you need to obtain a Certificate of Public Convenience and Necessity. This is issued by the DOT. Second you need to meet the technical requirements in Part 121. This is known as OP SPECS and is issued by the FAA.
Many things are considered in the Certificate of Public Convenience and Necessity. You must show that the airline is fit, willing, and able to provide the service. On the financial side, you must show that you can operate for the first 90 days without any revenue. You must also show enough capital for five years of operations. You must show that your management team is qualified and capable, and that your aircraft choice and routes are compatible with your plans. Finally, you must show that the airline's owners meet the citizenship requirements.
For OP SPECS you need to put together a comprehensive Operating Manual, Training Manual, and Maintenance Manual. After these are approved by the FAA, the qualifications of the airline's senior technical staff will be examined. The FAA will check aircraft histories and look at individual maintenance programs. If you outsource maintenance, the maintenance provider must be FAA certified for the types of aircraft you operate. Finally, you crews must be current, or training to be current in the aircraft types you plan to operate.
I hope this helps answer some of your questions.
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