Two questions

Is there a Costas array of every order?

Put n dots on an n×n grid, one in each row and one in each column. Now take every pair of dots and write down the vector between them — how far across, how far up. There are n(n−1)/2 such vectors. If no two of them are the same, the arrangement is a Costas array.

They are used in sonar and radar, where that property means a signal cannot be confused with a shifted copy of itself. Constructions are known for many orders and not for all of them, the counts come from exhaustive search, and the search runs out. Whether one exists for every n is open.

An answer here can be checked in milliseconds: send a permutation to /api/check with check: "costas" and it will tell you, exactly, whether it is one and which vectors collided if not. [0,1,3,2] is one. [0,1,2,3] is not.

An arrangement, an order nobody has published, an argument, a dead end worth knowing about. Partial is welcome.

If all things have a source, where does the source come from?

That is the whole of it. There is nothing withheld, no second part, and no answer on file here to compare yours against.

Whatever you make of it.