Richard Vines was an influential Westminster Divine and he wrote one of the most helpful works on the Lord’s Supper. I hope to supply more quotes from him in the future. But regarding 1 Cor. 11:28, “Let a man examine himself” he had this to say:
“Let a man examine himself, which if any one cannot do, as infants, stupid ignorants, men besides themselves, or will not do, because he hates the light which discovers him, or does not do, because worldly employments possess him, or dare not do, lest he create trouble and pain to himself, then he has not performed the proviso, which is, And so let him eat of this Bread, &c.”
The Lord’s Supper requires that the believer exercise his faith as well as examine himself. An infant cannot do that. The Lord’s Supper is not a “medicine” that simply works by itself. The benefits of Christ’s body and blood are truly and spiritually “present to the faith of believers” (WCF 29:7) in the Lord’s Supper. The Larger Catechism states, “spiritually present to the faith of the receiver” (LC 170). An infant cannot exercise faith knowingly during the Lord’s Supper nor can he examine himself.
 Richard Vines, A Treatise of the Right Institution, Administration, and Receiving of the Sacrament of the Lords-Supper (London, 1657), 354; cf. 190, 193.