Them who? The CONUS?
The first Soviet ICBM was under initial testing that very year, 1957.
The first submarine launched Soviet missiles were deployed in 1960.
What remains is the long-range strategic bomber force. Now, the Tu-95 had just been introduced in service, I don't know how operational it was in 1957 and in what numbers. Other heavy bombers could reach the CONUS by way of the North Pole, but not without using a small number of subpolar airfields in Siberia, and ISTR that these were on the US laundry list of pre-emptive targets.
Make no mistake, the Soviets could make central Europe, and a number of areas closer to them, places to avoid for decades. But I really doubt they could do the same to the CONUS.