(1) Description of the phenomenonIt may be an incorrect appoach to try to extrapolate the age of the Grand Canyon from present erosion rates. The Grand Canyon may have formed rather suddenly.
The major Mt. Ste. Helen's eruption took place in a few hours. Yet the aftermath was such, that future scientists, if they were unfamiliar with the history of the phenomenon, might think that the resulting geological formations required millions of years to unfold.
Sedimentary rocks are produced when materials dissolved or suspended in a transport medium (usually water) settle out and form a layer of precipitate. Any moisture in the sediments escapes (desiccation). During or after desiccation chemical reactions among the particles of sediment cement them into rock (lithification). The longer the period of sedimentation, the thicker a layer of rock will be and the longer the required period of lithification. Sedimentary rock formation can be observed today, and it produces rocks just like the ones we see layered in places like the Grand Canyon.
(2) Why this phenomenon indicates an ancient earth
The average thickness of sediments on the North American continent is about a mile, though in the Appalachian Mountains it is five miles. These rocks display anywhere from scores to thousands of discrete layers. For multiple such layers to form, a period of sedimentation must occur, then the transport medium (wind or water) must be removed, then lithification must take place, then another layer of sediment must be laid on top of the first. Lithification is a chemical process which proceeds at a relatively slow rate, with no known method of making it go faster. From observed rates of sedimentation and lithification it is calculated that, even allowing for periodic catastrophes, it must have taken millions of years to form the sedimentary rocks on the North American continent. For example, the Redwall Limestone found in the American Southwest is 700 feet thick; the known rate of lithification of limestone would require 1.6 million years for that layer alone, after deposition was finished. Furthermore, the Redwall formation had several thousand feet of sedimentary rock laid on top of it after it hardened. There are canyons such as the Grand Canyon cut through these sedimentary rocks. So the layers of rocks must have formed first, and then wind and water cut the canyons. The Grand Canyon is a mile deep. Even assuming numerous catastrophes, it must have taken hundreds of thousands of years for the Grand Canyon to be cut after the sedimentary rock had formed.
(3) Could the great deluge explain this phenomenon?
One flood cannot produce multiple discrete layers of sedimentary rocks. Without lithification, a new layer just mixes with the one already there (some sediments display signs of this mixing, showing that the layer in place did not harden before the next layer was laid). How can the great deluge, in the span of about one year, have deposited a layer of sediment, retreated while the sediment hardened, returned to deposit another layer of sediment atop the first, retreated again while that layer hardened, and so through many layers of rock, and then poured retreating floodwaters through the resulting rock to cut a canyon a mile deep? If the sedimentary rocks and the canyons cut through them did not result from the natural forces that we see forming them today, then they are a sheer miracle performed by God.