I just purchased a Trek Verve 2 fro the local bike shop. I found that I can't take my hands off the handle bars for an instant because the front wheel veers left. After a hysterical and disappointing phone conversation with the "builder" at the shop, I'm no wiser. After the builder gave me a safety lesson on why I should never take my hands off the handlebars because I then can't access the brakes, he told me "some bikes never ride straight because of the bike's geometry." He then doubled down by telling me to look it up. So....I did. I've read that it's probably either a bent frame, the seat-tube and forks are not in line, or there's an issue with the forks. Can anyone out there tell me HOW to determine what EXACTLY is the issue?Or is this an issue a good biker builder can address and resolve?

Seems like the easiest thing to do is to bring your bike back to the same shop and ride another Trek Verve 2 or similar bike momentarily handsfree in front of the alleged "builder", right?

The most obvious and simplest reason would be the front wheel is not sitting in the dropout properly, so check that.
It sounds like you should find another bike shop. A bike should track perfectly fine with no hands.