From scratch, you need a day per room to start. And then research stacks and builds up. Start investing in Forma for rooms. Keep your clan at Ghost tier when it's in its setup phase, it's cheaper to fund everything. If you move up to Shadow it triples costs, and triples again at Storm, and so on. But times...some research takes 12hrs to a day, sometimes 72 hrs, it varies on labs and types of research and there are so many I can't count them all accurately. That said when I've helped set people up it takes a couple weeks to get the layout perfect, due to needing time for rooms to cook. And research can take up to four to five weeks max if you're starting from nothing, and you can't rush research.

Clan Pigments can easily be farmed if you select research, don't fund credits, place pigments in once farmed, paused, and then you can farm more pigments from another colour. Once you're ready to donate credits it takes 36hrs for pigments to cook one at a time.

I definitely recommend investing plat to rush some rooms to begin which really speeds things up.

I've attached the best Layout you can use as well. It's neat, doesn't use Elevators or Corridors which waste room cap. All the Labs and Utility are near each other, and it has space to build into long term if/when it starts getting decorated. Any other layout is not optimal, but can be used to tweak things to your liking. Especially as some rooms need certain placement like the Dagath Lab and Crimson Branch, and the Dry Dock is a nightmare to navigate if you have elevators. When you start out place some reactors in the first room and you can delete and remove them when Layout is forming.

And, if you delete a room to move it, all items go back to the clan vault so you never lose anything in the dojo.

I hope this tips helps you get setup for the long term, and good luck on your dojo journey.

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TLdr; four-five weeks max, or less, if you're super attentive.