Welcome to FT!
MUC is set up so that each gate can be used as a Schengen or a non-Schengen gate, so there are different levels -- one for Schengen flights, one for non-Schengen.

When you exit the US flight, head for the center of the terminal along with everyone else, where you will pass through passport control, and before coming down to the baggage area, you will turn right to "connections", pass through the security check along with other departing passengers and head into the Schengen level, where you will then find your gate and board the plane. This is tight, but doable in 30 mins assuming the flight is on time. Otherwise, after passing security head to the customer service center and they'll put you on the next flight.