Russian rating labels at Sinop

Were any first-rate ships present at the Battle of Sinop?

Yes, according to the brief answer, although the later fleet list uses a different rating label for the 84-gun ships.

Both first rates and third rates are identified in the Russian order of battle. Later, the three 84-gun ships are called second rates, while another three ships are listed with 120 guns each. The inconsistent labels make the gun totals firmer than the rating categories. Sailing-era categories therefore need to be checked against the underlying armament and the terminology used by each navy.