Michael Barrett wrote some great follow-up commentary to the aforelinked Back to Work episode on feeling like a fraud:

…after a while you adjust to the new normal and it becomes real and true.

When you step into a new role or arena it sometimes takes a while to realize that everyone else in there is just like you and that you fit in just fine.

Relatedly, this Steve Jobs quote:

Everything around you that you call life was made up by people that were no smarter than you.