No, that won't be built in three years. I believe you grossly underestimate what kind of resources, funds, and manpower would be necessary to get this done.
Dreadnoughts are the largest combat vessels built by Council species. They're about one kilometre long. By comparison, the Reaper capital ships are 2km.
As of 2183, the turians had 37 dreadnoughts, the asari had 21, the salarians had 16, and the Alliance had 6 with another under construction. As of 2185, the dreadnought count was 39 turian, 20 asari, 16 salarian, and 8 human. By 2186, humans construct a ninth dreadnought, and the volus have built a single dreadnought of their own.
Since the Alliance only had one dreadnought under construction in 2183, but two more in 2185, they must have finished an entire *new* ship in the space of two years. The Turians built two more also.
In 2186 the Alliance had three more dreadnoughts than in 2183.
As for Normandy-class frigates, the Alliance had managed to construct a second one by 2185, SSV Ain Jalut. It was mentioned in ME2.