An excellent way to see the Grand Canyon in a single day is via Scenic Airlines: just under 10 hours in total. Their shuttle bus will pick you up at your Vegas hotel in the early morning, and drive you to their own small air terminal. Their plane, which has floor to ceiling windows, will give you spectacular views of Hoover Dam, Lake Mead, and of course the Grand Canyon itself. The plane will land near the South Rim, and you'll have 3 hours to roam the South Rim on your own. (You'll also be provided lunch). Then they'll fly you back to Vegas, and their shuttle bus will take you back to your hotel. I've done this tour twice, and remember the tour as one of the most spectacular experiences in my life. For details, see
https://www.scenic.com/tours/grand-canyon-connoisseur