I'm not personally familiar with Google's culture, but I came to USDS from AWS, and you're right that government work culture is pretty different from what you would see in the private sector.
One of USDS's core values is "Go where the work is," and we embed people with expertise in agencies to work on those agencies' priorities. Frequently, that means joining existing projects and working within the agency's culture (while also pushing that culture to be more flexible when necessary). USDS engagements tend to have a lot of support from agency leadership, and USDSers tend to learn ways around agency practices that get in the way, but we're very much joining and working within an existing, government work culture in each engagement rather than importing our own.
One of USDS's core values is "Go where the work is," and we embed people with expertise in agencies to work on those agencies' priorities. Frequently, that means joining existing projects and working within the agency's culture (while also pushing that culture to be more flexible when necessary). USDS engagements tend to have a lot of support from agency leadership, and USDSers tend to learn ways around agency practices that get in the way, but we're very much joining and working within an existing, government work culture in each engagement rather than importing our own.