Will we ever find out ?

I believed the Catalyst designed it and fed organics in multiple cycles. Someone else suggested the Leviathan designed it and had their thralls build it. In either case it was likely worked on by long dead races who had evidence of their existence scraped away post-Reaper invasion.

There was a thread asking what people thought what the dlc would be, which later was the Citadel dlc. I wanted a crucible dlc.

When the thing says "you do not know them, and there's not enough time to explain" is what I would say is Bioware's way of saying we have no idea. We just put it in the game for...reasons. The thing does mention it knew about it several cycles ago. So it didn't know about the plans for very long even though vendetta says that countless cycles before added something.Than it says it thought it was gone. Which to me is odd it would say that since the protheans were building it during their time. They were sabotaged from within. So the thing had to of known about it since the ones who sabotaged the project were indoctrinated.

Leviathan says it was never completed. I'm guessing the protheans were likley the only one's to even start building before being sabotaged. In our cycle we're able to build it. Had the relays been working during the prothean cycle, I believe they would have been able to build it and deploy the crucible. Again. That's guessing on my part

If I had to guess who designed the initial plans, I would say the keepers. They know the Citadel inside and out. In order to have plans to build something to work with the citadel, someone had to know the ins and outs of the Citadel. If it wasn't them, no idea.

I like this idea somewhat... modified such that the Catalyst made the initial design with a different motive in mind (e.g. maybe to make harvesting even easier/quicker so that he oculd gather more data faster (which is what Leviathan said his purpose really was - to scour the galaxy for data)... and then it was modified by the organics in one cycle as a means of trying to destroy him and his Reapers.  It didn't work, of course, and the Catalyst thought he had destroyed the plan... but like bad breath, the plan kept showing up in subsequent cycles despite his best efforts to destroy it... and it kept getting modified and made more powerful.  The species that kept modifying it in each cycle kept finding ways to ensure the plans would survive into the next cycle should their iteration of it not work (just like Liara was shown doing with her little device)... leading to his comment about how resourceful organics are.