Beck, a Kennesaw State senior who won the 2013 Georgia State Amateur and finished second in the 2014 Georgia Open, tallied seven birdies against one bogey to shoot 65 on the 7,374-yard, par-71 Highlands Course.
Horsfield, who advanced to the quarterfinals of this year's U.S. Junior Amateur, shot a bogey-free 66 on the companion stroke-play course, the 7,437-yard, par 72 Riverside Course. Moore, a University of Arkansas junior, made seven birdies and one bogey for this 66 at Riverside.
"It feels so good. I've been playing well coming into this, and just to see putts fall, continue to fall and just hit it where you want to hit it, it's a good feeling," said Beck, a first-team Atlantic Sun Conference pick in 2013 and 2014. "I was just really trying to have fun and end the summer right and what better way to do it than right here in Georgia?"
The 2014 U.S. Amateur Championship consists of 36 holes of stroke play followed by six rounds of match play, with the championship scheduled to conclude with a 36-hole final on Sunday.
Brisbane golfer Taylor MacDonald is the best of the seven Australians at the completion of the opening day, MacDonald's round of 3 under par 68 at the Highlands Course, seeing him in a share of 7th position and three from the lead at the end of day one.
MacDonald is currently Australia's third highest ranked player in the world amateur rankings behind Lucas Herbert and Geoff Drakeford and is playing his second event of the summer in the US having played very well at the recent Western Amateur.
Tomorrow MacDonald will play the Riverside Course at the Atlanta Athletic Club, two courses being used in the opening two rounds.
"I've been here (in the US) - this is my third week now. I had a Houston camp, and a Golf Australia camp as my service providers, and then I have had two homes to stay, families, one for the Western Amateur and one for here.
"This (the Highlands Course) is probably more a bomber's golf course. You need to get it out there and give yourself less to the green if you're going to lay up, obviously. But you've definitely got to hit driver well and long, and I'm starting to do that, so it's good."
Curtis Luck and Lucas Herbert are the next best of the Australians in 105th position, Todd Sinnott 168th with Jarryd Felton and Ryan Ruffels a distant 207th and Kade McBride even further back.