After the first round in McKinney, Texas, Kim, 16, tied for 53rd place after making five birdies and an eagle.
The amateur would be the fifth-youngest player to make the cut at a PGA Tour event if he advanced past round two.
Kim stated that although the circumstances were “quite simple,” he would “absolutely accept” his score because it was his first time.
With an eight-under 63, Wallace, 34, took the lead from a group of seven players by one stroke.
The Englishman, who has failed to make the cut five times this year and has not finished in the top 10 in eleven events, says he is attempting to pick up tips from some of his younger opponents.
“I notice that many of them, particularly the younger guys—I’m not too old, but younger than me—are really focused on their shot and don’t care about the result or what other people think,” Wallace said.