Now, big disclaimer, I am very sceptical they would go there and they have been vague on if Bran can really change the past. Plus, Iam assuming Bran has not intentionally conspired to drive Dany insane early so that the realm turns on her. But, what else can you do.
So Bran was able to warg Hodor in the past and was able to speak to Young Ned at the Tower of Joy. These imply he can manipulate the past.
The way I see it there are two moments Bran could use such powers to prevent the massacre at Kings Landing.
1 - He wargs Danys dragon. Then, he lands the dragon in the courtyard of the Red Keep with all the people. Now Dany has been stating, arbitrarily, for several episodes that the people of Westeros do not love her despite having never interacted with them (Northern Lords and POW do not count). Plus, she did burn them but only when they were specks of dust from her perspective. If Dany landed, she would realise the error of her ways and you would have another Mhysa moment as her people embrace her.
2 - Bran stops that Wight getting the killing blow on Jorah. He can do this by warging ghost and intervening. This means that Jorah is merely grievously wounded. As Dany doesn’t want to leave his side until he recovers, she never makes the premature journey by sea to Dragonstone and so Rhaegal and Missandei never die. This time Dany hears the bells and doesn’t go mad because she hasn’t lost all her friends. She lands in the Red Keep courtyard and her people embrace her.
Because at the minute it looks like the show is determined to have the worst ending ever in my opinion. Plus, Bran kind of needs to do something beyond be a meme.