I just happen to be writing an extensive paper on Central Park right now…so I will try to keep this really short…
The OP makes a very common mistake in assuming that CP is UNDEVELOPED land. It is anything but. It seems like a natural landscape that has been lined with paths, etc. but it is an entirely artificial landscape.
By the 1860s, the lower part of NY was getting very crowded. New ideas about the value of parks and open space were emerging. The elite classes of NY wanted to create a park which would a)mitigate the crowding that was taking over lower Manhattan, b) provide recreational opportunities to all classes, and c) serve a didactic purpose, essentially teaching the working classes how to recreate in a genteel fashion.
After much wrangling, it was decided that the new park should be in the location where it is now. This was far north of the population center, but the planners chose it because it was cheap. Why was it so cheap?
a) There was little development there already because it was…
b)undesirable land–swampy, rocky, ugly–a dumping ground. The only people who lived there were…
c) poor immigrants, squatters, the homeless, and barnyard animals. Who could not really protest their displacement.
In spite of these facts, the fact that the planners made it so large is truly remarkable.
To make a very long story short, a contest was held to plan the landscaping of the park. Frederick Law Olmstead and Calvert Vaux won. One of the main things that differentiated their plan was that they planned that the cross-streets, which were necessary to carry traffic from the upper west to the upper east side, and vice versa, were sunk BELOW grade level, so that they would interfere only minimally with the park experience that Olmstead and Vaux were trying to create.
To create the Central Park which we know now, the swamps had to be drained, huge amounts soil had to be trucked in, and artifical hills were built. Needless to say, all the trees and plants were new, too.
CP is big only in relation to the land mass of Manhattan–it is not that big compared to other large parks in the US and the world. One of the reasons why you can walk through CP and see all the beautiful vistas and scenes is because Olmstead and Vaux planned it that way.
By the 1870s, the park was largely complete, and had a huge influence on urban park planning worldwide.
If you want to know more, read The Park and the People by Blackmar and Rosenzweig. Is is one of the most readable of the CP histories.