At age 23, Marquez competed in the first Miss International pageant held in Long Beach, California in 1960, becoming the first Miss International, and also the first Latin American titleholder in that line of pageants. During the press presentation at the former Lafayette Hotel, Marquez openly declared that she preferred to wear a figure-tight swimsuit that would showcase the pageant body she worked hard to achieve rather than the loose playsuits sponsored by the pageant organizers. She won the first evening gown competition out of the three rounds (1/3) at the pageant. Her measurements for the swimsuit competition which paved for her victory was recorded at 95—62—95 at exactly 170 centimeters. Ultimately, she won the title and received the following grand total prizes: