In the 1st week of Overlord the Allies put better than 350,000 troops (roughly 36 DIVISIONS) across the beaches. In under a month that rose to a shade over 1.2 million or roughly 100 divisions and 225,000 vehicles.
At it's peak, the USMC had just under 485,000 men, including airwings, making it larger than most of the world's armies. logistically, the USN tail need to support it was nearly unimaginable.
While I can understand the desire to make something really big, it is fairly critical (at least if it going to be posted in this forum, where there are more than a few folks who know Amphibious operations) that you get a good understanding of the requirements of a major landing.
If, as one might surmise from the way the scenario is presented, this is the invasion of the United States by a victorious CSA in the 20th Century the logistical effort required is overwhelming. To just put 100,000 foot soldiers, no supplies, no vehicles, artillery, armor or anything else will require 2,500 LCVP, assuming that none are lost to beach defenses, a better figure is 3,500 - 4,500. You will need close to 1,000 LCT to put the armor, jeeps, artillery, ammo, rations, and the rest of the minimal supplies to support the assault troops for a day. Figure an minimum of 200 escort & gunfire support vessels ranging from corvettes up to battleships, times that by two -three if the USN is still a going concern. Unlike the Normandy assault, it would be a six hour trip back to reload supplies, meaning you will have a need for at least three times the cargo bottoms that the allies managed.
I would suggest that it is logistically impossible for any even barely realistic CSA to muster that sort of force. The population could not support a military force that large. It takes anywhere from 1 to 1.5 men afloat for every man you put onto the beach at any time, meaning you would need 1,500,000 sailors to put one million troops on the beach (a figure equal to that put ashore by the allies in the first month of Overlord). That would require a population of at least 20 million, assuming you go to a total war footing and have every peron you can working on production or in uniform, and that the entire military is concentrated in that one place. If you have more forces, you will need more people, and in the scenario it would seem you will need a LOT more troops. That is going to be tough for a CSA with a starting population of just 5.5 million in 1865 (slaves wouldn't be of much use in factory settings & the chances of a free black population in ANY CSA is bizarre in the extreme). Even allowing for a full doubling of the literate population needed for industrial work every 20 years (something of a question prior to modern medicine) that would only leave 88 million white population best case. That size population won't support a 300 division size military (100 divisions or 1, million to invade, 40 divisions to defend what must be a heavily fortified border, and 1.5 million (= to 150 divisions) navy and a minimal 100,000 member Air Force) not if it also has to provide the tools of war.
The allies cheated at Normandy because they had to cross a strait, one that could effectively plug at each end, not an actual body of water where every ship required escort on every trip and the forces that would, in this scenario have to be offshore on AKs were sitting in camps in England. The massively reduced the number of ships and sailors needed to invade Western Europe. Without that accident of geography the Allies would have needed many times the number of ships, with a corresponding increase in the number of ship's crews.