"Pushing" an age origin (he's pushing 30)

What is the origin of saying “he’s pushing x years old”? Like “he’s pushing 30” or “she’s pushing 40”?

Well, I’d imagine that “dragging 40” would imply the person’s already past 40. “Getting near 40” is just something most people I know–and especially me when I was in my 30s–didn’t want to hear because it was too sharp a reminder.

The question, for no discernible reason, reminded me of something that happened in my neighborhood when I was a kid. There was one lady, evidently not all there, who wasn’t “all there.” She was at every neighborhood event because, of course, she lived in the neighborhood and it would’ve been a tad tacky to not invite her. At one such event, my mother heard the woman say to someone else, “I’m really looking forward to 40!” Mom said to the lady next to her, “Hmm. She must be facing the wrong direction.”

The OED seems to imply that it may be derived from “to strive after something” (e.g., “Signor Nitti has made a mistake by pushing for an immediate solution.”). The use would be somewhat ironic: “He’s trying hard to be forty” when you don’t really have to try.