You know the old saying, "Never say never".
However, I think it is safe to say that with very few exceptions, using stairs at a moderate pace will not be harmful.
It's always a good idea to ask your vet, but actually, the sort of (rare) physical conditions that could cause problems are not going to discovered at their early stages in a typical routine vet examination. Also, there are some breeds that have a tendency toward those sort of conditions - your breeder or breed rescue would be the one to ask about that
That having been said, there are a few things to be aware of.
- Puppies - and adult dogs that haven't been exposed to them, - have to be taught to use the stairs. With puppies, there are many sources all over the web that will tell you how to do it. Some adults - notably rescue greyhounds, but it could be any rescue dog - know nothing about stairs, so they have to be taught as well.
- Again with puppies, try to keep the use of stairs to necessary uses at a moderate pace. Don't use the stairs as a plaything. Puppy growth plates can be injured by too much or too fast climbing and jumping.
- With all dogs, be aware of the potential for injury. Large dogs especially. Dogs can and have suffered sprains and muscle injuries on stairs. Be aware of obstructions, turns and the like that could be problematic. Also, some dogs have a tendency to jump the stairs - or jump some steps - going down. That is another potential for injury.