I will be receiving a three-year-old Golden Gate Ficus
If it's only 3 years old, it will take years of growth and training before it can become a bonsai.
I’ve been reading a lot about propagating bonsai from cuttings
You don't propagate bonsai from cuttings, you propagate plants or trees. These then can be trained to become bonsai. This, again, requires many years of growth and training.
Can a cutting be acquired from ANY tree
Any tree or shrub that is suitable for bonsai and that can be propagated by cuttings.
I be better off trimming from preexisting bonsai?
This will make no difference. A cutting from a bonsai (if left untouched) will grow out to a normal tree. Taking a cutting of bonsai probably takes even longer, as the cutting will be small.
Please let me know if this is too advanced a practice for me to be taking on this early. Thanks in advance!
Cuttings you can get for free, so why not. Just don't expect you'll be able to grow them into bonsai any time soon.
Try to get more mature material to save a couple of years.
Seems you are really new, so I suggest you start studying - there's a lot of information on this site.