[RPG] use the Booming Blade/Green-Flame Blade cantrips from hiding and still have advantage (for Sneak Attacks)

So as long as you qualify for Sneak Attack, it applies. In your example, the melee attack would trigger Sneak Attack.

You can even get sneak attack on an opportunity attack later in the round because it's only limited to once per turn. Sneak attack is not an attack action, it's a triggered event based on its prerequisites.

The official Sage Advice Compendium confirms this:

Can you use green-flame blade and booming blade with Extra Attack, opportunity attacks, Sneak Attack, and other weapon attack options?

Introduced in the Sword Coast Adventurer’s Guide, the green-flame blade and booming blade spells pose a number of questions, because they each do something unusual: require you to make a melee attack with a weapon as part of the spell’s casting. First, each of these spells involves a normal melee weapon attack, not a spell attack, so you use whatever ability modifier you normally use with the weapon. (A spell tells you if it includes a spell attack, and neither of these spells do.) For example, if you use a longsword with green-flame blade, you use your Strength modifier for the weapon’s attack and damage rolls.

Second, neither green-flame blade nor booming blade works with Extra Attack or any other feature that requires the Attack action. Like other spells, these cantrips require the Cast a Spell action, not the Attack action, and they can’t be used to make an opportunity attack, unless a special feature allows you to do so.

Third, these weapon attacks work with Sneak Attack if they fulfill the normal requirements for that feature. For example, if you have the Sneak Attack feature and cast greenflame blade with a finesse weapon, you can deal Sneak Attack damage to the target of the weapon attack if you have advantage on the attack roll and hit.

(This answer addresses booming blade and green-flame blade as they were prior to the 2020 Errata of Sword Coast Adventurer’s Guide and may no longer be applicable to the current official version of these spells)

The meaning of "melee attack with a weapon" is different from the meaning of "melee weapon attack". So long as what you use is a weapon (including improvised weapons, but not unarmed strikes) and you make an attack with it, you have fulfilled the precondition. You can even use a ranged weapon (as an improvised weapon) to make a melee attack using these spells.