You should always consider the wider context. Unusual phrases that you cannot find in a dictionary may be explained in the surrounding text.
I found the quote, from the short story The Third Level:
Sometimes I think Grand Central is growing like a tree, pushing out new corridors and staircases like roots. There's probably a long tunnel that nobody knows about feeling its way under the city right now on its way to Times Square and maybe another to Central Park.
You will see I have highlighted the simile - the writer says that Grand Central Station is "like a tree", and describes its tunnels like "roots". Roots of a tree grow underground, and so your phrase in question is just a continuation of this simile, imagining that tunnels are "feeling their way under the city" as if they are roots of a tree finding new pathways. Of course, this latter part is abstract - the original simile is quite sound to describe the real network of tunnels, but the idea that new ones would "grow" is pure imagination.