I'd say the age of domain is one of the top factors in obtaining "authority" status. And then within the age factor are all the other things that determine its age. Change of owners. Change of IPs. Change of Servers. Change of just about everything that takes place within DNS.
I also feel that "stability" in the hosting network is another factor. I feel that anyone who has a serious Internet business is going to have their own IPs and possibly server(s) to do their thing. They won't be relying on a cheap web host to compete in a market that is reserved for the BIG BOYs. That's like showing up for a drag race in a Prius or something. ;)
It is not the "only" factor though. Success takes time. There was a point in Internet history when it "could" happen overnight but that has slowly dwindled to lotto type statistics. You'll have to invest the time and patience knowing that what you are building is a long term proposition.
Sure, you can open your doors and have success overnight and it still happens. If you have the right product and/or service along with a few strategically placed marketing efforts, you can start the ball rolling. Nature will take its course from there. Yes, things will "naturally" happen as it goes viral. Unfortunately many of us may not reach that level and we'll continue to work in the trenches, feed our families, and make a decent living off the leftovers. :)
Yes, domain age is an important factor in "all" things Internet related. Each year that passes, the value of that domain increases. It's like fine wine. Since 1995 has a bit of meaning when talking Internet these days. Companies who have been online for any period of time would be wise to start advertising their Since dates.