You can walk that much if you are healthy, have roads, have enough food and water, good clothing and shoes, there are no dangers that must be avoided and if you know what your destination is. If you have to stop daily to get food (hunting or gathering fruit), avoid or fight dangerous people and animals, figure out best ways to get along while carying whaterver possesions they had, shelter from bad weather, prospect for places to settle permanently or temporarily then it's a completely different story. It's also not like they had a deadline or something.

Centuries is a lot of time, you can do 1km a day looking for food and in 5000 days (~14y) you're there. Or you can go forward 10km, go back 5km every once in a while and it will still take you less than 200 years to do that.

If then you add multiple generations, you can absolutely do it.

I believe the logic was this: with horses, they would have had the upper hand in warfare against the Neolithic farmers and hunter-gatherers that they encountered. It's not the speed of transport per se.