This might be Second Ending by James White. The Wikipedia Entry doesn’t have a lot of detail about the story; there is more about it on Goodreads
This story is a long time favourite of mine. In it, a young man is awakened from suspended animation. He is in an underground hospital, the surface of the earth having been devastated by several atomic wars. He had been placed in suspension due to illness which has been cured during his suspension. He is the last man alive and has been awakened by robots who have used a painted bust of Beethoven to simulate a human being.
The man sets about exploring the world and looking for other survivors. The surface of the world is completely sterile. He gives his robots directions - to make themselves more intelligent and build their skill sets, to search for and nurture first any humans, then (when no humans are found) any life. Through all of this he is haunted by his memories of his girl friend Alice, now long dead.
When his food supply runs out he goes back into suspension and is awakened centuries later to find the world covered in grass, grown from some seeds found sticking to the clothes he was wearing when he came to the hospital. As the story progresses he starts to sleep longer and longer into the future while the earth, and later the sun, change. At his penultimate awakening the robots place him in a spaceship and send him off into space. Finally, he awakes when the spaceship lands on another planet orbiting another star where he finds a race of human like creatures who all look very similar to Alice. He realises that the robots have fulfilled his last request.