A century is not such a long time for many races of Faerun. Elves, dwarves, gnomes have significantly longer lifespans and even some halfelves and halflings can live that long. So you could imagine there will be survivors of ToT still alive and able to tell stories. How well do we know about WW2 nowadays? I would take that as an example.
"I was a young acolyte at the House of Wonder in Waterdeep when the gods walked beside us. I had just turned 15. The senior priests were praying and receiving no response from our Lady. It was such a scary time, but it was also one of the reasons I got into adventuring afterwards. That and a simple bar brawl that let me meet my good old friend Formentera. Well, not that he is really old, he still has not made his third century yet. But look at me, even my half blood is no longer enough to keep me from feeling ancient.
Anyway, you wanted to hear about the Time of Troubles, right? Afterwards we learned quite a bit through our prayers. You see, Ao made all gods explain what happened to their faithful. There was even a cult to Ao founded in Waterdeep at that time. We quickly came to regard Midnight as a human avatar of our Lady. I say quickly as I was not one of the old guard at that time. Ah the good old days..."
Sources for this description: FR Adventures, Faiths and Avatars