There are only 5 parts to the SS and you have to transport those parts to your capital once they're built. So your 5 best production cities, provided their close to the capital for the fastest build and launch.
SS Factory for SS parts; Factory, Windmill (on flat ground), Solar Plant (near desert), nuclear plant, hydro plant (near river) and railroad connecting to the capital all boost total hammers. Some folks have posted that the forge boosts the SS parts as well, because apparently they're considered as land based units. If you can get a Golden age when you start building the parts that'll help too.
If you have excess food and your citizens are working a non-production tile, you can make them unemployed to get 1 hammer out of each of them. Of course Factory, Windmill and Workshop let you run the citizens as Engineers which gives 2 hammers now that the patch fixed that. If you built or captured the Statue of Liberty, that'll make all specialists, including unemployed citizens, provide one extra hammer each.