Normally no. But in the right circumstances, yes.
In most cases, a creature is assumed to be moving around in its space on the battlefield, not fixedly focused forward on one opponent (that's suicidal, for exactly the reason you present). So, normally, no, you can't just walk around an opponent and get advantage on them: they see you, see where you went, and are keeping an eye on you.
The exceptions happen in, well, exceptional circumstances, as judged by the DM's good sense. To demonstrate, I have to make something up, so let's have an example.
You meet an man in the forest. He challenges you, drawing his sword.
Suddenly your warlock companion throws a curse at the him, acting quicker than the drawn sword. You've seen this before, it's an eyebite curse. The man collapses, asleep.
“What was that for?!”
“We're looking for those old ruins, right? He might know where they are. No sense killing him out of hand just because he's jumpy. Get around behind him and be ready to hit him if he causes trouble.”
You stand a close behind where the man fell as the warlock shakes the man awake, and gets right up in his face, holding his attention. “That was impolite of you. Shall we start over?”
There, in that moment, you're not hidden. You didn't have to make a hide check to get there, but notice how you're out of the target's sight. This is an example of not being seen.
The DM's judgement is very important in 5e, for exactly this reason. Most of the time it will be obvious: you're not hidden, and the target can see you just fine. In rare circumstances — often, circumstances that you've put some work into creating — you'll be unseen despite not being properly hidden, and then you'll have advantage if you need to put a knife in their kidney without actually hiding.