"I would love to hear what atheists call these manifestations instead"
Hey Soft and Gentle I call it a case of the vapors (which was a Victorian Society statement for a heat flash, dizziness or a touch of who knows what).
To be serious for a moment I actually call those manifestations........ inspiration, serendipity or even spiritual (Not god related but listening to Mozart or standing in a Trout stream making a cast).
"Serendipity. Look for something, find something else, and realize that what you've found is more suited to your needs than what you thought you were looking for."
"The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!', but 'That's funny…'"Isaac Asimov
“Whether we name divine presence synchronicity, serendipity, or graced moment matters little. What matters is the reality that our hearts have been understood. Nothing is as real as a healthy dose of magic which restores our spirits.” Nancy Long
And if you can't experience that........ a glass of brown liquor will help get you there.
Gio