The expression definitely refers to baseball, yes. Not sure if "man up" is exactly what is meant, unless you're using it in the sense of "prepare for stiffer competition, challenge oneself harder."
Yes, it is a baseball reference. In America, most baseball players start in the minor league and if they are good enough, they are invited to "step up to the major league."
So, it means that it is time to take on a bigger challenge. Actually, it is more than just a bigger challenge, the biggest challenge of all. When one steps up to the majors, they are playing with the best in the wo