The definition out of rules of the sneak attack is
Beginning at 1st level, you know how to strike subtly and exploit a foe's distraction.
But following the rules, you can only use sneak attack if you have advantage on the attack or if another enemy of the target is within 5 feet and you don't have disadvantage on the attack.
Does this mean that if the Rogue catches an enemy surprised at the beginning of the first round, he cannot use the sneak attack unless he has advantage?
Since a Rogue with the Assassin Archetype at 3rd level will score all critical hits against a surprised target, and with the new rules the critical hits "If the attack involves other damage dice, such as from the rogue's Sneak Attack feature, you roll those dice twice as well."…
Best Answer
Normally, you would be correct; if a level 2 Rogue (or level 3 rogue of any other Archetype except Assassin) catches an enemy by surprise or takes their turn before the start of the targets initiative count, they would also need Advantage on the attack for it to apply Sneak Attack. A level 3 Rogue with the Assassin Archetype get's the Assassinate feature, however, which does the following.
From PHB pg 97
The first part is important because it already grants you Advantage, which means automatic Sneak Attack against any creature that hasn't taken it's 1st turn yet. This applies whether or not you have surprised your enemy, but if you happen to do so, your attack is also a critical hit. If you can surprise your enemy AND go before them in the initiative (because surprised enemies still roll Initiative and have a chance of going before you) then you A. Have advantage on the attack against them (Sneak Attack), and B. deal critical damage with all damage dice (Assassinate)).