rather a problem of having 350M people. Your solution is completely impractical. You cannot test everyone. Even if all those tests were available (they aren't and won't be for a long time), there is 0% chance you could get everone to be tested, and to be tested in a way where the timing works out well enough that we could isolate the infecteds to eradicate this thing. We would also need the rest of the world to completely buy in. Your solution is impossible.

The only ways to beat this thing are 1) a vaccine (which won't be ready for at least another year), 2) herd immunity by "letting" the healthiest and least at risk among us get sick, or 3) a treatment (HCQ/azythromycin if it's effective or something like that). Since #3 doesn't exist currently and #1 will demolish our economy and so many people's livelihoods, #2 is the only option that is practical enough to work, although it does require accepting the fact that a small % of people will die, but no more than would die from the normal viruses we see every year.