I am reading a book on this very subject right now. By Michio Kaku "To win a nuclear war." It has a kind of leftist bent, and clearly tries to portray the US as the big evil aggressor (IMHO a tad unfairly). However, it is based on FOI requests and it seems rather accurate.
It details several scenarios with a US first strike.
The earlier in the Cold war you get, the more likely it seems. There are several reasons.
Reason 1) less Soviet retaliation capability means war planners are more willing to give it a go.
Reason 2) MUCH less concern the earlier back you go about civilian casualties. Also, nuclear winter wasn't really considered.
Reason 3) Anti-war and anti-nuclear movement was less of an issue before 'Nam.
So, as for some interesting scenarios, ripped right from the book. (and from history). There are more, but these are my favorite.
Scenario 1: 1953 - Korean war: Peace talks with North Korea and China do not have the critical breakthrough that they had in our TL. As a result President Eisenhower implements OPLAN, which called for the use of tactical nukes on North Korean positions. Soviets declare war resulting in the US implementing its "massive retaliation" plan of dropping hundreds of nukes on the USSR.
Scenario 2: 1954 - Dien Bien Phu - Rather than rejecting the offer of two nukes, the French accept the US offer of two nukes to stop the Viet Min at Dien Bien Phu. Using nuclear weapons in 'Nam starts a cycle of escalation leading to ww3, with the US launching first.
Scenario 3: 1961 - Berlin Crisis: JFK, after satellites discover that the USSR has only four, rather than the hundreds of ICBMs that Khrushchev was boasting, opts to KO the USSR in a crippling first strike. (in our TL this plan was rejected because of concern that too many Soviet bombers would still get through, killing millions of Americans. In this TL have the planners be more optimistic about our air defense).
These are all pretty fun and interesting and are based on actual historical plans.