Doctor Who rewatch: The End of the World, 1.02
The beginning is at the end.
As their world burns up in the future, prefiguring how she herself will burn like the sun, he holds out his hand and she accepts. They both begin to save each other.
It’s also significant that this is the episode where the Doctor starts to, in my opinion, fall for Rose. This is also a nice echo of “time can be rewritten,” which may also be why the Doctor won’t let Rose continue in her despair. Her sadness and despair for people she will never know are understood by the Doctor, because he feels them too, and because he feels what she is feeling, he knows how to help her.