Rosenstein was a George W. Bush appointed US Attorney for the Maryland district at the time of the inauguration; he was not in the DOJ top hierarchy. He was actively nominated by President Trump for the Deputy AG job in early Feb 2017. When there was a mass firing of US Attorneys in March 2017, Rosenstein was excluded from that as his nomination for DAG was still pending. He was thought to be a good Republican law and order guy. As they say: mistakes were made ...
Trump did not know Rosenstein.
Sessions recommended Rosenstein and Trump went along with the recommendation.
One more example of Sessions screwing up and using poor judgement.
Or maybe, Sessions sabotaging Trump.