I wonder if there exists a sci-fiction that talks about how human beings detect something disastrous happened to Sgr A* and realize that happened 26,000 years ago then try to leave the Milky Way in panic.
Yes, there is. But it isn't humans who first discover our galaxy's core explosion, but Pierson's Puppetteers (1). Fun stories by Larry Niven in his "Known Space" series.
(1) https://en.wikipedia.org/wiki/Pierson%27s_Puppeteers