I can see what you think of Atlanta's chances.
You're right, I don't think much of their chances, even with the series now tied. Honestly yesterdays game, though the end was much closer, reminded me a lot of Game 4 of the Bulls vs Hawks in 2011.
But for records sake...
Atlanta last made the Finals as the St. Louis Hawks in 1961.
They made the ECF in 2015, their first appearance in the conference finals since 1970, when they belonged to the Western Division, and it was known as the Western Divisions Finals. Their first two years in Atlanta they made the Division Finals, 69 and 70, and were beaten into a pulp by the Lakers both times.