Mindfulness is a human quality. Because I first came across mindfulness in the writings of East Asian Zen Buddhists, I got the idea—wrongly—that Buddhists more or less coined the concept. Here's a quotation from a French Renaissance essayist, Michel de Montaigne that gives good expression to the practice of mindfulness arising in France in the 1500s:
And, needless to say, one could find countless other expressions of the practice of mindfulness in every human culture throughout all time. (And, I strongly suspect if we were able to perceive it, we would discover that the wisdom of mindfulness practice pervades all life forms.)
"When I dance, I dance, when I sleep, I sleep, yes, and when I walk alone in a beautiful orchard, if any thoughts drift to far-off matters for some part of the time ... I lead them back again to the walk, the orchard, to the sweetness of this solitude, to myself." —Michel de Montaigne
The essential point is to cultivate mindfulness right here, just now.