What would have to happen for a giant tidal wave to wash its way around an entire planet? The planet can be like earth, with the same size, mass, and everything else. However the wave must start without an impact from space.
It sounds like you're asking for a phenomenon similar to the waves in Interstellar - a periodic and regular wave that sweeps across the surface of the planet. In that case, your use of the term "tidal wave" may have been remarkably prescient, because you're actually looking for tides.
Tides literally are waves that sweep across the world. Without any landmasses in the way, we would have four bulges of water sweeping across the planet surface, two from the Moon and two from the Sun. So, in order to have a planet with the same mass and size as Earth that has tides sweeping across the surface, cover the thing in water.
Now, that didn't feel like I answered the spirit of the question. On an Earth like ours, could we make this happen and retain the landmasses? Well, tidal height is linearly proportional to mass and proportional to the cube of distance. The average height above sea level for continents is 800 meters. On Earth, the average tide height is ~1-2 meters. To increase that by 400x, we'll need to move the Earth to about 1/8th of its previous radius. That puts us well within Mercury's radius and would probably just melt the planet whole. That's why a black hole was used in Interstellar to obtain a similar effect - maximizing the mass and minimizing the heat produced.
The largest tsunamis that are anticipated by natural causes, not including meteor impacts, occur when there are large landslides. The greatest of these include large sections of continental shelves. There is a large continental shelf off of western Africa that is expected to collapse some time in the future. The tsunami will be tremendous and obliterate many cities.
HOWEVER, I don't believe that even the worst case scenarios would generate enough wave energy to carry a large body of water across an entire continent with two mountain ranges (e.g. North America with the Appalachians and Rockies.)
Do you want the giant waves to be regular, predictable phenomena, or sudden catastrophes happening only once in the history of the planet and destroying everything?
1) Make a planet with very flat continents - I can't think of a reason to have continents that are very flat, but there must be some. Or make the continents all submerged except for small, flat atolls that barely break the surface.
2) Make it a very young planet that has a very young and very large moon. The moon has recently formed and is still very near to the planet.
Dubukay's answer says that tidal height is linearly proportional to mass and proportional to the cube of distance.
At present the Moon is about 384,389 kilometers from Earth. If Earth's Moon was still only a tenth as far as it is now, the tides would be about 1,000 times higher. If Earth's Moon was only a fifteenth as far away as it is now, the tides would be 3,375 times as high. If the planet's continents are small and flat, the tides might sweep completely over them two times a day.
Of course the moon was believed to have formed in a gigantic collusion that would have exterminated any life on Earth. If your planet has a very young large moon that recently formed in the same way, the planet could not have advanced lifeforms that took billions of years to evolve, and you may desire them for your story.
3) Make the planet a moon, a satellite of a gas giant planet that orbits in the habitable zone of their star. Earth has 81.300813 times the mass of the Moon. The gas giant planets in our solar system have masses that range from 14.6 times the mass of Earth (Uranus) to 317.8 times the mass of Earth (Jupiter), and thus 1,186.9918 to 25,837.398 times the mass of the Moon.
So if Earth orbited a giant planet like those in our solar system at the same distance (384,389 kilometers) as the Moon orbits Earth, the tides the giant planet caused on Earth would be 1,186.9918 to 25,837.398 times as high as lunar tides on Earth. If you arbitrarily move the planet out to about four times the distance of the Moon, or kilometers, the tides would be one 64th as high, but still 18.5467 to 403.70934 times higher than lunar tides.
Astronomer have discovered giant planets in other solar systems that are several times more massive than Jupiter. Of course a Earth sized moon orbiting a giant planet should become tidally locked with one sized always facing the planet. Thus the tidal bulges one opposite sides of the moon would stay in the same places instead of sweeping around the world. So method of preventing the moon from becoming totally tidally locked to the planet would be necessary.
4) Make the planet orbit very close to its star to have giant tides. Dubakay in his answer claimed that if the planet orbited close enough to its star to have giant tides, the planet would be sterilized by the heat of its star.
But if a star is very dim, a planet would have to orbit very close to it to receive the same amount of heat and light as Earth gets from the Sun. According to the list of potentially habitable exoplanets, the four potentially habitable planets orbiting in the habitable zone of the dim spectral type M8V star TRAPPIST-1 have years ranging from 12.4 Earth days down to 4.05 Earth days. Their distances from TRAPPIST-1 range from 0.02888 astronomical units (AU) to 0.0451 AU, or about 4,320,386.4 to about 6,746,863.9 kilometers.
If TRAPPIST-1 had the same mass as the Sun, its four potentially habitable planets within its habitable zone would have tides ranging from about 10,900.168 to 41,515.227 times as high as solar tides (not lunar tides) on Earth. But TRAPPIST-1 is less massive as the Sun. The mass of TRAPPIST-1 is about 0.089 the mass of the Sun, so the tides created by TRAPPIST-1 on its four potentially habitable planets should range from about 970.116 to about 3,694.8596 times as high as solar tides on Earth.
Since the Sun's tidal attraction on the Earth is about 0.4727 that of the Moon, the tides created by TRAPPIST-1 on its four potentially habitable planets should range from about 458.573 to about 1,746.5601 times as high as the Moon's tides on Earth.
Of course it is expected that the planets orbiting in the narrow habitable zone of a class M star would be tidally locked to their star. Thus the tidal bulges on opposite sides of the planet should be motionless. A way to keep the planet from being tidally locked is needed.
If the planet orbiting close to a dim red star is actually a giant moon orbiting a giant planet, it should become tidally locked to the giant planet and thus avoid being tidally locked to the dim red star. Thus it would have days as long as the months of its orbit around the giant planet, and the giant tidal bulges created by the star would sweep around the moon.
Anyway, those are my thoughts about how to have periodic giant water flows covering the small and very flat continents of an otherwise Earth like planet.