The Bureau: XCOM Declassified (Xbox 360)

It's 1962. John F. Kennedy is the U.S. President and the Cold War has the nation gripped with fear — but a far more viscous and insidious enemy than communism is threatening America. Known only to a scant few, a covet government unit called The Bureau begins investigating and concealing a series of mysterious attacks by an alien enemy. As special agent William Carter, you make the decisions, pull the trigger and lead your squad in a third-person tactical shooter set within a high-stakes, covert war to defend the human race. The Bureau's mission is clear — survive, adapt and overcome the enemy threat (Heartbreak Ridge-style) to protect the citizens from the truth.

https://www.metacritic.com/game/xbox-360/the-bureau-xcom-declassified