"A while ago" is some time more than a few minutes, but you don't know (or cannot be bothered remembering) how long.

"He left here a while ago - fifteen minutes, an hour?""President Kennedy was assassinated a while ago - forty, fifty years?"

"Quite a while ago" is some time more than a few minutes, but you don't know (or cannot be bothered remembering) how long, but is longer ago than something.It could be longer than some period already mentioned, or longer than the speaker thinks the listener would expect, or longer than the speaker originally thought - possibly other implications.

"Did he leave recently?" - "Oh, no. It's quite a while now - fifteen minutes maybe."Child asks, "When was President Kennedy assassinated?" - "It was quite a while ago, before you were born. Forty or fifty years ago.""When did he leave?" - "A while ago ... (thinks ) ...well, quite a while, probably an hour ago."

*******************To say in a short and colloquial way that "a little time has passed from the moment he came out", I would say something like:-

"He came out here a short time ago.""He came out a little while ago""He came out not long ago.""He came out to see me just a bit ago.""He came out just a while ago."