How does a conceit opening a metaphysical poem relate to the era's focus on carpe diem?
Conceits are elaborate comparisons relating two unlikely things, such as John Donne's famous metaphysical conceit comparing love to a geographer's compass ("Valediction: Forbidding Mourning"). Metaphysical poets were learned and intelligent, so the topics of metaphysical poetry are serious in nature and touch especially on the nature of love, the relationship between God and humanity, pleasure, and art. The concept of carpe diem, introduced by Horace, cautioned against drawing hopes on a very distant future because events of the future are largely unknown. The concept instead advances the idea of focusing on the near-future and the present time at hand.
Conceits opening metaphysical poems relate the topic at hand to the present moment or the moments of the near-future. For instance, Thomas Carew's conceit in "The Spring" contrasts the breaking up of winter and the unveiling of spring with the cold, hard pitiless feeling in his love's heart. This conceit connects the metaphysical topic of his love's heart to Carew's focus on carpe diem, represented by the present and near-future in which winter is breaking and spring is blooming:
Time with the season : only she doth carry
June in her eyes, in her heart January.