what about a U/S for pyloric stenosis--doesn't sound like a classic story and it's been a few years since I saw a bunch on my peds surgery month, but I thought they usually present around week 4-6
Certainly worth thinking about, and you're right about the time frame, but the story doesn't fit well. Unfortunately the term 'projectile vomiting' has made it into the public vocab, so it seems every kid you see has it. I generally ask if it looks like the Exorcist vomiting.
Either way what you generally see is a kid who forcefully vomits pretty close after a feed, then is quite hungry again. It's also usually a baby with poor weight gain and electrolyte abnormalities, though that's only if it's been going on for a while. So I'd ask what this kid's birth weight was, and see what his weight is now. Sometimes, if there's a question, I'll check a BMP (you want a straight stick, not a heel stick), but this single episode of vomiting probably wouldn't make me get an u/s.
Could it be an early presentation of PS? Possibly, so you need to make sure they follow up with their PCP or come back if the vomiting gets worse, more frequent, that sort of thing. Even if you did the u/s now, it wouldn't show up.
If we had gone to the ED every time the above happened to us, our (healthy, happy) 3 yo would have spent more time in the hospital than a sickle cell CFer with ALL.
The "work up" should have included a call to the pediatrician's advice nurse and ended there. Bummer that it wound up in your lap.

Welcome to my world.
That said, I pretty much never chalk vomiting up to a 'GI bug' in this age group. There are too many other things you have to prove they don't have (malro, obstruction, hirsprung, sepsis, pyelo). Plus, your typical bugs would probably warrant admission for a 30 day old given how quickly they can dehydrate and run into problems.
The most likely explanation is reflux though at least with the available history. Child abuse should always be on the radar too if the kid is irritable/fussy. Cardiac stuff can also cause vomiting, so you'd want to make sure the kid isn't sweating or turning blue during feeds or tiring out during his feeds.
Some people worry about an ALTE (acute life threatening event) and whether this represents an ALTE and if it does, how much you are obligated to do. I hate ALTEs and it's a very subjective call. Usually 'stopped breathing and turned blue' is the phrase I looked for to admit them, but even then I have a hard time believing most of the stories I get (he stopped breathing for 5 full minutes! I was going to start CPR!). If that's the case
you should at least consider a sepsis evaluation, though it's probably overkill.
Anyway, that's probably way more than anyone wanted to hear. I'd be curious if there's more to the story. What did you do, Wilco?