Games played before the regular session is played

a Garage Sale patron who shows up prior to the posted start time of the sale

A bingo game played before the start of a "session". But sometimes the Early Bird game is merely the first game of the session. The first game of a session is more commonly known as a "Warm Up". See definition of "session".

a person who gets up very early in the morning

a person who arrives early before others do

a number that appears before its own counting place