Game Face (1971)

“Out on the field, Brooks Robinson, the object of all this attention, tried to keep wearing his customary game face, the pleasantly serious one, but it was no use. He finally had to break out laughing, too.” Milton Richman (UPI), “Everyone Cheers for Brooks,” Paterson (NJ) News, October 12, 1971, p20
NOTE: The term was widely used as early as the 1930s, especially in football but also in basketball and even golf, but except for a couple of school and minor league examples did not seem to catch on in baseball until much later.

No earliest use given in 2009 Dickson Baseball Dictionary