I agree that this subject is too broad and needs to be narrowed down. You don't really need a "topic sentence" if all you're going to do is spew facts.
What you should do, although it doesn't sound like this is your assignment, is pick an aspect of the cold war and discuss how it affected life (politics, culture, science, etc.) in the United States. For example, a lot of the space program in the beginning was all about the cold war. The USSR had put a satellite into orbit before we had; we needed to get to the moon before they did. It also changed education in the United States--what we were doing wrong, that they had a satellite before we did? This led to things like the "new math" and a push to recruit people to become teachers. Etc. Politics: JFK campaigned on the idea of a "missile gap," which actually didn't exist, but it was very effective and you could get a lot of things done by scaring people about the USSR.
Even movies reflected the cold war mentality.
You need to narrow this down, and you need to pick a topic that can be discussed--this should not be a listing of facts.