The owners, executives and coaches of the fledgling New York City FC, one of two Major League Soccer expansion franchises set to enter the league in 2015, say they want to win right away. But three months before their inaugural match, they still need to find the vast majority of their roster.

Major League Soccer allows each team a roster of up to 30 players. So far, NYCFC has eight—six domestic players with MLS experience who count against the $3.1 million salary cap and two aging European legends (David Villa and Frank Lampard)...