You may have to define the average man, cause by region that varies widely. Though I am sure a man about 5-5.5 ft and around 130-145 lbs in reasonable shape, would be plausible on the larger breeds. (Imagination required for this to work). https://www.akc.org/dog-breeds/largest-dog-breeds/ I recommend a robust and powerful doggo, over one that is simply large but spindly.
I've been told Tibettan Mastiffs might be able to support the weight of man, since they're about the size of a small horse, but I don't think that's true, they look too fluffy for that to be an accurate size estimate.
Maybe hooking a pair up to a chariot would be more advantageous use of large dogs as mode for transportation.
True, which is acknoledged, dog carts do exist. But do you think, with maybe some mix of breeds, a large enough or strong enough dog for.. let's say a 5'10" 140 lbs man to ride without aid?
Not with out some genetic manipulation, to ensure that you get the best out of all the traits you desire in a riding dog. So the taller and more muscular you can design a mixed dog, the better off you will be. Though there is a type of cow that is bread to be lean, and has bulging muscular body as a result of an early form of breeding selection, so it may be possible in that low tech way to try all kinds of combinations until you get the dog that suits your purposes. https://en.wikipedia.org/wiki/Belgian_Blue
I've seen enough to believe that they can be used as mounts for long distances, same as horses. They are stronger but slower. If you want a quicker mount but not horses, look at Mules and donkeys. I remember years ago reading about a cavalry soldier for the Confederacy riding a donkey (can't find it now).