Doing a coast to coast trip as your first trip, some have done it and for them it was a great trip. But I like to work up to bigger challenges instead of starting out with the big one first.
Do a trip with ACA, they have several trips that are a week long.
https://www.adventurecycling.org/guided-tours/
On some of their trips you haul your camping gear on the bike, some of the trips are van supported and they haul your luggage in a van from campsite to campsite. I can't think of a better way to build confidence than to ride with a group for a week. Many if not most in the group will have been doing it for years.
Last year I did a trip with ACA in Big Bend TX. That trip was over spring break for one teacher that was in our group. They might have other trips that are close enough for you to drive to instead of having to fly to. The first ACA trip I did, I rode Amtrak to and from it.