I believe it is possible for countries to open up short of massive testing. However, that requires that they took swift and dramatic actions early in the spread - early testing, strict quarantines, early shutdowns, and widespread adoption of masks. the first countries to open up handled the early onset extremely well and can now re-open. The places that did this were the same places that were hit the hardest with SARS - notably China, Hong Kong, Taiwan, Singapore. Because the virus was well controlled from the outset, they were able to contain and can move on.
Unfortunately, becasue of the size of our country and our current penetration rate, we have to test much, much more than they had to. Had we been testing at the rate South Korea was when the virus was initially spreading, our current position would be much different and much less testing would be required today.