I don't know about osx, but for at least for ubuntu it could be as easy as
/etc/init.d/postgres start to get it started. (Which was your objective, right?)
Even if it is not auto-started, the control scripts tends to be present.
If you still need to find the directory, you could try a file search for some file found in the data directory - e.g.
(assuming locate is available on osx, something will be)
It may turn up some false positives, such as wherever it is copied from when you create a new one, man pages, etc, but I think the list should be short enough that you'll have no problem finding it.
One of my postgres clusters has this data directory: