In what way is "The Passionate Shepherd to His Love" an expression of the philosophy of carpe diem. Carpe diem is Latin for "seize the day": meaning take full advantage of present opportunities. This sentiment is found not only in classical literature but in much of English literature as well (e.g., "Gather ye rosebuds while ye may" and "Had we but world enough, and time, / This coyness, Lady, were no crime").

The poem is an example of the genre in that the passionate shepherd is encouraging his lover to seize the moment and make the fateful decision to be with him forever. There's no sense in which he wants her to think things over. As far as he's concerned, he's given her every possible reason to make this life-changing decision and doesn't see why she should hesitate a moment longer.
The problem for the shepherd, of course, is that his lover is immortal, and so time means nothing to her. She can take as long as she likes; there is no moment for her to seize. And, as an immortal nymph, it's unlikely that she'll be impressed by all the earthly goods that the shepherd has to offer her—from the beds of roses to a belt of straw and ivy buds adorned with coral clasps and amber studs.
https://www.poetryfoundation.org/poems/44675/the-passionate-shepherd-to-his-love