The only way the CSA could surpass the USA if it it somehow took over the USA's northern industrial base and, consequently, the Great Plains and West Coast. Any modern industrialized state that covers most of North America is going to be a great power, for a huge number of reasons.
Now, I have no idea what needs to happen for the CSA to take over the USA. As UoBLoyalist correctly stated, no plausible CSA victory would overshadow an existing USA. So let's suppose arguendo that ITTL the CSA does somehow take over the entire USA and move on from there.
What if ITTL the CSA has a Communist Revolution at around the same time as Russia's OTL Communist Revolution? Note that in OTL the Civil War ended in the 1865 and the Russian Revolution happened in 1917. Obviously the CSA would remain an agrarian slaveholding society for as long as the white ruling class would be able to maintain it, and I think it's reasonable to argue that it could maintain its oppressive system for fifty or sixty years before being at serious risk of collapsing. And given the tenor of 20th century liberation movements around the globe, a revolution against the CSA would definitely draw from Communist ideas. (I also like this idea for the silly reason that "CSA" can also stand for "Communist States of America.")
I think it's plausible for the Romanovs to avert a revolution and successfully reform. Nicholas II OTL tried to do just that but was defeated by various factors that can to some degree be mitigated. And if we see one or two World Wars reasonably similar to those OTL, there could easily be an ersatz Cold War between a liberal democratic Russia under a constitutional monarchy and a revolutionary communist CSA.
The big questions here are: how can the CSA absorb the USA? And, how could the World Wars shake out so the Central Powers lose anyway?