The United flight from Newark arrives in Terminal 1 / Concourse A.
The building that houses the A concourse also has the Z concourse, which is the floor above the A concourse. When you arrive on a flight from an out-of-Schengen airport, which Newark is, you normally go to a gate in the Z concourse. (I believe buses from an aircraft the deplanes on the tarmac go to a gate on the lower, A level, of the building, but you can't get into the rest of the A concourse without going through passport control.) I don't know how you would get from a Tarmac bus gate to the Z level. I'm sure a worker on the bus or at the gate will be instructing passenger who need the Z level on how to do it.
To walk between Concourses Z and C, you would have to go out of security and into the "public" part of T1, which would require you to go through Schengen immigration (passport control) and then back through Schengen emigration (another passport control).
To avoid going through passport control you will have to stay in the part of the airport that is called "airside". You can do this by taking the rooftop Skyline shuttle train between the concourses.
Each car on the Skyline is designated either "landside" (inside Schengen) or "airside" (outside Schengen) and the doors only open to the landside or airside of a Skyline station. The C concourse only has airside, so you can't access concourse C from a landside car.
The Skyline station for the A/Z concourses has a landside part connected to A and an airside part connected to Z.