Even if they fall in your fireplace, they still can be reunited with their parents. If you cannot reach that location, just close off the fireplace with a close fitting fire screen or cardboard. Then, cap your chimney to prevent reoccurrence. Only rescue a baby bird that is weak, cold, sick or injured. Rescue is also appropriate if you know the parents are dead, or if the baby bird is in immediate danger from dogs, cats, fire ants, children, etc.
Shoeboxes work well for tiny birds.
You can create a makeshift nest by putting a small dish or butter tub lined with paper towels. It is not necessary to use the original nesting material. Check the box frequently for the appropriate temperature. The bird should feel warm to your touch, but not hot. Put it in a dark, quiet place.