If you are good with potted plants and have patience you can do it. There is a lot of time spent doing nothing except basic care, watering, fertilizing regularly and keeping an eye out for trouble. Most growers end up with more than a few trees so that they can spread their enthusiasm.Some of them are absolutely beautiful. I could get hooked on these. I must read up on them to see if I have the patience and more importantly, the intelligence to try this.
In your area you can grow species that I cannot at least not easily. I have some Ficus and a Live Oak that cannot tolerate the winters here. I tried an Olive once, not the true Olive but Budicia, but had no luck with it.
Be advised that most of those fine old trees that you see are collected, you are not likely to create something like that from small material. Keep an eye out for old landscape material that is being removed, these can make good bonsai. If/when you are ready, post in the bonsai forum.