Pilgrim,

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How can one "hear the gospel" unless they are antecedently regenerated? Are those who are regenerated at baptism, particularly infants who survive into adulthood, saved immediately?

Calvinists stray into Arminian territory with their Order of Salvation. If man must first be regenerated before he can "hear the gospel" and believe, then salvation is not monergistic. Under Calvinism, salvation is a process where God does His part (effectual call) and then Man does his part by responding to the call and is thereby saved.

Lutherans do not separate regeneration and justification. Thus, salvation is completely apart from any cooperation of man. Through the means of grace (Word and Sacrament), God gives all His gifts at once. He calls, regenerates, gives faith, enlightens, and saves. Man does not respond; he receives.

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And are such individuals required to repent and believe upon Christ at some time consequent to their baptism?

We are simultaneously saints and sinners. The Christian life is one of daily repentance and faith.