In "The Dalek Invasion of Earth" she leaves the First Doctor to live on Earth with David Campbell. Which would have meant that she escaped the Time War.
In "Father’s Day", the Ninth Doctor states that his family was killed in the Time War and in "The Doctor’s Daughter", the Tenth Doctor reaffirms this. Clara claims that the Twelfth Doctor had once had children in "Listen".
The new series points to the idea that the Doctor’s family died in the Time War. But with Susan settling on Earth, she wouldn’t have died in the War. She lived long enough to meet the Fifth Doctor in "The Five Doctors" and the Seventh Doctor in "Dimensions in Time".
