@ArchUDBA, There are several routes to becoming a licensed architect in the U.S. The fastest is to get a 5.0 year Bachelor OF Architecture degree (BArch).
The second is to get a 4.0 year BA or BS IN architecture, architectural studies, art, art history, environmental design OR ANYTHING ELSE then go to graduate school for a Master of Architecture (MArch). With a BA/BS, an MArch takes from 2.0 to 3.5 years depending on your undergraduate degree and your MArch program.
As far as I know the schools on your QuestBridge list that offer a BArch are Rice, Notre Dame and USC. They all require or recommend a portfolio as part of the admission process. These schools also offer the BA/BS+MArch. The BArch is an intensely focused professional degree that requires a high level of commitment to architecture and doesn’t allow much room for exposure to other disciplines.
Several others have Schools of Architecture, but only offer the MArch. Their undergraduate BA or BS architecture programs are integrated with their architecture schools, but most don’t guarantee that you would be admitted into their MArch programs. These would be Columbia, MIT, Penn, Princeton, UVA, Yale.
Others do not have their own School of Architecture, but have strong BA/BS architecture, art and art history programs and a good track record of getting their graduates into top MArch programs. Some of these would be Brown, Oberlin, Stanford, Vassar, Wesleyan, Williams. Basically, you can get into a top MArch program with an undergraduate degree in anything from anywhere, as long as you fulfill the MArch requirements and have a strong portfolio.
If you decide to get a BA/BS + MArch, think about how you will finance the MArch. Grants are available, but they are not as generous or predictable as undergraduate scholarships.