"The player's listed in the starting lineup must meet certain requirements before they can be substituted for (i.e. pitchers must face at least one batter, batter must take 1 AB)."
What rule set are you talking about? Those certainly are NOT ASA rules, and the initial question said the game was under ASA rules.
Two things you should know. The players are officially in the game when the line-ups are approved in the pre-game conference, and (two) players can be substituted for anytime the ball is dead without any requirements for having physically participated in the game.
Ref: 3.4.1.A and 3.4.1.A.1. Also 3.4.6.A and 3.4.6.C
WMB
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