Despite the always reliable summaries of facts that the anybody-can-edit Wikipedia has (/s) the problem with steel radioactive contamination is not nuclear bombs that have not been exploded in the atmosphere at all since 1980, and mostly before 1964. It is cobalt-60 radiation sources that get melted down into steel with some regularity, and the fact that virtually all steel in commerce includes (contaminated) scrap steel, even when a batch is mostly from freshly mined ore.
When producing fresh steel the industry, using conventional blast furnaces, decided to monitor erosion of the lining by putting Co-60 sources in the brick lining, and when the Co-60 disappeared (because it had gotten melted into the steel) they knew the lining needed to be replaced. So adding radioactive contamination was part of the production process. This is still done is some places, but mostly the Co-60 now comes from sources used to measure the thickness of steel, and every so often one of them ends up in the pile of scrap to be remelted.
But it is accurate to say that the contamination of steel started with the nuclear age because before 1945 there was no Co-60 to contaminate the steel with.