So there are two issues to consider, and my original answer only considered one of these. I can't find a definitive answer, but interpreting RAW to answer:
Issue One: Does a Verbal Component Spoil the Hidden Advantage?
Short Answer: GM's Call
There's no general rule I can find which dictates how loud/obvious verbal components are. There's a couple of specific spells, but nothing general. So it's a GM's call as to whether the verbal component can be heard and understood to be an attack. I'd err on the side of the player in most cases, esp if combat is already underway; the noise of combat would probably cover most verbal components.
If the GM rules the noise reveals the warlock, then none of the attacks will have advantage.
Do Separate Attack Rolls from Eldritch Blast All Use Advantage?
Again, there's no RAW which definitively answers this. But we can infer an answer using two other rules:
Attacking while Hidden, PHB, p195
When a creature can't see you, you have advantage on attack rolls
against it. If you are hidden-both unseen and unheard-when you make an
attack, you give away your location when the attack hits or misses.
Eldritch Blast Cantrip, PHB, p237
You can direct the beams at the same target or at different ones. Make
a separate attack roll for each beam.
Since you're making a separate attack roll, you give away your location on the first roll, so you'd have advantage on the first, but not on the subsequent rolls. There's no wording to suggest the two (or more) blasts are simultaneous.
As a GM, I can imagine a circumstance where a player might convince me otherwise. But that would probably be outside of RAW.
So, in the specific case of your Goblin Warlock, It's GMs call if the first attack gets Advantage, but the second should definitely not.
A lot of D&D is the GM making calls like these. The rules are pretty good as a baseline, but far from comprehensive.