You show your total ignorance on geology and just facts in general. The river's elevation is about 2000 ft while the South Rim is at 7000 feet, almost a mile higher. It is known that the area of the canyon is or has been rising (didn't have time to find out which). The massive amounts of debris that used to go through the canyon every spring (before man built dams) would carve the the canyon as the land rose.
A smaller example is evident where I live. I live east of SF bay about 10 miles inland. The land is about 350 ft in altitude, while at the Bay it is about sea level. In between are a range of hills about 1000 feet high, formed between the Calavaras and Hayward faults. There is a creek, Alameda Creek, that drains the whole area where I live into the Bay. How did it get over the hills? The easiest and most sensible explanation was that the creek existed when the land was relatively flat. The paralell faults have squeezed the land between them to produce the hills. In Niles Canyon, where the creek flows, the hills are hundreds of feet high with almost vertical sides. You drive through it next to the creek. How else could the creek have gotten over the hills? Using GPS stations, they have shown that the land is rising. Day by day, the canyon is getting imperceptably deeper, based on the hills rising and the creek eroding.
This is happening on a much larger scale at the Grand Canyon.
Water is flowing downhill now, and water flowed downhill then, Wacka. Some things don’t change. A river changes course, or becomes a lake, until a higher elevation is surmounted. Rivers tend to follow geological faults for this reason. Erosion is associated with volume and speed of water, the characteristics of the substrates underlying it, or both.
Rivers are fed via numerous sources; rainwater, snowmelt, springs, etcetera. There is a geological concept known as the “Continental Divide,” most prominently on the west coast, but there’s also an eastern one, which runs through my home state. On the east of that divide, water flows downhill, generally and inexorably to the east, with rare exception due to unique topography. On the west, westward.
Funny how that works.