I got started with deliveries as a part time "delivery captain" for a Sea Ray transitioning to a Marine Max dealership.
At a dealership (well at least the one I worked for), most of the "delivery captains" are the people who introduce the boat buyers to their new boat. Their job is to go over the boat anchor to transom, and then give some limited instruction on how to dock/handle the boat. Some people wanted and paid the dealership for extra hours of instruction.
After a year or so of this, my reputation for knowledge and instructional ability caused many of the customers and the dealership to ask me for help inside AND outside the dealership to move vessels all over the Northeast and up and down the coast to Florida. That in turn started an avalanche of people wanting help or outright for captaining their boats or at least ride along for jack of all trades help.
I do have to say that most of my customers would up commenting that they chose me, not because of boat handling skills or systems knowledge (plenty of captains had those). They found my background in USCG aviation safety, attention to detail, and keeping my word important. So just maritime skills are important, but so are qualities many of these successful business people looked for when hiring people.
Another smaller help was my wife, who at the time was a real estate salesperson. Whenever she sold a waterfront home, she asked about whether there was an intention to buy a boat. If the answer was yes, she gave them a gift certificate for 4 hours of boat training from me. That helped, mainly for training and private captain gigs.
Lastly, my job as a NJ Boating Safety Certification instructor and an instructor for USCG captain's licensing also spread my name by word of mouth and landed me more work than I wanted as a "retired guy".
The biggest issue I can see with being a delivery captain is being away from home. Even though it was normal for me with my other career, now being retired (at least semi)... to earn a living as a delivery captain was not really an option. On those trips where my wife came along and for the occasional out of town cruise on someone else's budget was pretty sweet so part time was good.
On the subject that often gets discussed on one's future in boating after a certain age....there are so many paths. Between deliveries and the assistance towing job, I had enough water time and boat use to sell all of my boats and dabble in the RV world for a few years early on in my life. The RV time back then became valuable to me now that I sold the trawler. Seeing the places I used to visit by boat now by RV is fun and allows me to go places the boat never could.
As the other thread concerning what to do when operating/maintaining your own boat becomes too much, there's certainly enough to do and for the boating fix, I did downsize to 2 smaller boats that can travel when I RV and one to fish hard when in Florida and not on the road.