Great Lakes Dredge & Dock Co. builds islands by a method called hydraulic dredging. If you have a couple million dollars, maybe they can build one for you (You get the permits, though).
Check out The Palm Islands which are artificial islands constructed from sand dredged from the bottom of the Persian Gulf by the Belgian company, Jan De Nul and the Dutch company, Van Oord. They are located in Dubai. They build islands. Really.
It would cost more than a few million dollars. I'm sure you have that because all island creators always use this forum. Don't talk to experts because you certainly can get every bit of the proper way to do it here. We all have dreams, some are attainable, others are more of a nightmare.
Simply buy 100k tons of sand, throw it in the ocean and plop down some plants, throw a few animals on your new island and WHA LA.