The 14-year-old Park from Eustis, Fla., led by three strokes at the 6,353-yard Echo Lake Country Club. Park, who came to the United States from Korea last year, had six birdies and three bogeys.
Chris Brady, whose mother won the 1968 tournament, was in second after an even-par 73. Mallory Code of Tampa, Fla., Taylor Leon of Dallas and Catalina Marin of Colombia all were tied at 1-over 74. Seven players had 75s.
The higher scores were a result of strong winds, which reached 15 mph during the afternoon, but Park missed just four greens.
After making the round of 32 in last year's tournament, Park lost to Eom Ji Park, another Korean, 1-up.
Brady is trying to join her mother, Peggy, as the second mother-daughter duo to win a USGA championship. Peggy was known as Margaret Harmon when she won the 1968 Girls' Junior at Flint Golf Club in Michigan. Kathy Cornelius won the 1956 Women's Open and daughter Kay captured the 1981 Girls' Junior.
'I don't really think about whether there is more pressure on me knowing that my mom has won this event,'' said Brady, who had three birdies against three bogeys. 'There are a couple of trophies that both of our names are on, and that's cool. There are a couple trophies that her name is on and mine is not.
'It's not really pressure, it's more incentive.''
After a second day of stroke play Tuesday, the field will be reduced to 64 players for match play.
The U.S. Girls' Junior is one of 13 championships conducted by the USGA each year, 10 of which are strictly for amateurs. The event is open to female amateur golfers who have not reached their 18th birthday before July 27, 2002, and have USGA Handicap Indexes not exceeding 18.4.