That trust was severely damaged when the FAA showed themselves to be incompetently incapable of controlling Boeing, and incapable of realising that by refusing to ground the planes after the crashes. This resulted in 300+ hundred deaths. Since then EASA and the Civil Aviation Administration of China have stopped blindly trusting the FAA, and have their own extra checks and processes applied. As an example, the EASA was involved in 737 Max recertification (unprecedented), and is involved in the 777X certification. CAAC also didn't recertify the 737 Maxes until months after the FAA did.
It will take the FAA and American aerospace decades to build back any semblance of trust.
When you buy an airplane, it is a 30 year relationship. The airlines listen.