I've had two, and neither was a real thing of joy. The first was exactly like yours - never saw it go in, but knew in my case it was a good shot. The second was at SFGC, in front of some architects and on the duel hole. We gasped the minute it left the club face. Somehow, good shot vs. right at the pin is somehow knowable.
However, I was my own typical smart ass self almost immediately both times - as soon as I found my ball/saw it go in, I turned and said "Your shot is good!"
It may be that I know no matter how good, the ace is still a matter of luck. I was more exhilarated at my first eagle on a par 5, first time breaking 80, and my first run of 3 birdies in a row....come to think of it, except for breaking 80, the other two were only one time events for me.
The three birds was the most enlightening, occurring right after I had announced that I was giving up on my round. Not sure what that meant, but the minute score became unimportant, I started shooting lights out.