1. Industrial Scale Automation
There are a handful of spaceship factories in the Cosmic Era, large automated facilities that are able to rapidly built spaceships and launch them quickly and efficiently. Like the Federation's anchorage bases, these facilities are exclusively in space, where the automation can function without being impeded by gravity or corrosive atmospheric conditions. In these facilities, the ships are assembled, with the various sections welded together, and major systems installed. The non-automated crew work in specialized industrial hardsuits and construction mecha, allowing them greater mobility and precision than would be available to a crane or gantry operator. These massive ship factories allow for ship building potential that hasn't been seen since World War 2.
The key ship building yards in the Solar system are found in the Jovian system, under the dominion of the Atlantic Federation and the Seibertronians. There are also large yards above Earth, Mars, and in the asteroid belt. These are all dwarfed by Fimbulthul Spacewerks above Callisto. A multinational venture, Fimbulthul is joint operated by the Atlantic Federation, Pacific Rim Coalition, Kingdoms of Scandinavia, and New Seibertron.
2. Megascale Polyforges
The polyforge has revolutionized manufacturing in the Cosmic Era, replacing large factories with smaller factorums that work on an as needed basis, rather than building stockpiles and having large logistic chains for mundane and sundry goods. The Industrial Polyforges literally print the spaceframe and sub-components of the ships. The ships of the Cosmic Era are built as semi-monocoques, with twin pressure hulls, and load bearing shells. This is in contrast with the original method of building ships that saw the construction of a frame, and the rest of the ship built around this central frame. The forge printed ships are not as tough as the older method in terms of tensile strength and durability, but they are much quicker to make, and are built off of existing templates.
The printed ships are a compromise. Building frame up ships would take longer, and be more resource extensive, and building fully modular ships is also feasible but these ships lack the full rigidity and structural strength of a monocoque hull. These welded hulls are fully viable for marine ships, but in space, the large number of welds required to 'slice build' a ship are a serious liability.
The body of a ship is printed, but this method of construction isn't viable for highly complicated pieces of equipment. No one is printing AISC cores, drive engines, or dimensional reactor powerplants. These sub-components are manufactured elsewhere, in specialized facilities. This along with template construction allows for an engine plant to run at a steady pace and built up a stock of bulk engines or power plants, so that as hulls are completed, they can be fitted with the equipment instead of having to wait.
Ship building is a large and lucrative industry, and the hulls of ships are the least valuable, least complicated parts. A factory that produces or facility that stores engines, computers, weapons, etc, is going to be a major strategic asset. These facilities are well guarded, bunker-like, and have high classification levels. While people know that there are a lot of factories in the Jovian system, and that they are probably predominantly on Callisto, it is a large moon, and such things are easily lost.
Having a cybernetic race of sentient robots settled on Ganymede is an unprecedented resource. These beings are incredible builders, and are as capable as a larger force of humans in hardsuits and industrial mecha. They are engineers and builders, and in contrast to the mechaforming of Ganymede, building ships is a casual task.
The Seibertronians are a duel edged weapon, they are an independent faction, and are not restricted to working with or for a single nation. One of the key aspects of Federation foreign policy is keeping the Seibertronians placated and with positive relations.
Administrative harmony is an easily overlooked factor in the process. The process of ship building flows like water, with the various stages of automation and assembly being conducted like an orchestra. This has come from things like dream tank research, AISC coordination, the function of Mentats and other intelligence augmented humans, and meta-manager operations.
The operation of facilities like the Federation's Galax Yards above Jupiter operate with such efficiency that sub-assembly components can be maneuvered into place while the polyforges are still running. Over the production time of a ship, these efficiencies all add up.
6. Resource Acquisition
Spaceships take large amounts of resources, especially metal. The factions that are interested in ship building and station building, have space mining operations. All the asteroids being mined out for the metal by automated ships and independent mining companies provide a steady flow of refined materials to the shipyards and the factories, allowing them to build at a prodigious rate.
The exploitation of the Asteroid Belt and the various moons, and planets like Mercury and Mars, has driven the ship building industry. As resource exploration increases, it adds a need for more ships. More civilian ships and colonies need a larger fleet presence to protect them from pirates and foreign national hostility. Thus, more ships are built. The Battlestars are the current ultimate expression of this, and eventually something larger will appear to replace them, and builders are already looking toward what sort of ships will take humanity beyond the Solar System, or will settle exotic colonies in the most hostile environments.
There is a ship building race in the Cosmic Era, and it is an expensive race. The domination of space will belong to the nation with the largest number of ships. This has a number of parallels with Earth history, specifically the Two-Power Standard of the British Naval Defense Act of 1889. The Atlantic Federation has adopted this standard, to have their fleet be as large as the next two naval powers combined. In the Cosmic Era this means that the Federation fleet has to be as large as the combined fleets of the Pacific Rom Coalition, and the Machine Axis (Seibertron and the Five Metal Dragons). This ship building has the potential to bankrupt the powers playing the game.
The demand for ships has constantly pushed how quickly ships can be completed. Money and research keeps pushing for quicker and cheaper ways to build ships, and it is making progress. This has pushed other areas of research. Older ships are pulled from service and are recycled into new ships, or refit, or repurposed into something else.