That doesn't follow for me. If you surprise someone, they're unaware of your position, so you still get Sneak Attack and Advantage on your attack, even after their turn has come up and they've skipped it.
FWIW, I usually allow one character to start a combat with an attack roll if this degree of surprise is allowed (enemy not aware of your position, etc.) Then we roll initiative, placing that person at the top of the order. But that's just at my table.
Trit