I didn't really figure this out until I was sitting at Starbucks waiting for my beverage for the 20th time this week. Being the hot dog that I am, I like to draw attention to myself when I'm vaping and get reactions out of other people. Personally, I enjoy normalizing vaping, and I think that large, yet reasonable, clouds of vapor help to do this. That's why I don't stealth vape indoors. So the best way to produce that big cloud of vapor (without inhaling) is to deliberately inflate your cheeks as you suck in. Then, blow out right away. In other words, don't keep your cheeks inflated for more than 1-2 seconds. Don't allow the vapor to reach your throat because most of it will either get caught in there or travel down your windpipe. I recommend blowing out in a continuous motion. Whether it takes you 2 seconds or 20 seconds to completely exhale the vapor is irrelevant. It's only important that you begin the exhalation process within 1-2 seconds of inflating your cheeks.
Before I determined this, I was sucking in too quickly and most of the vapor was getting caught in my throat, and I wasn't creating much of a cloud at all.