Is there a proven theoretical lowest time complexity for the random generation of a Directed Acyclic Graph?

From my research, I could not find any "standard" (as in widely used) algorithm for the random generation of directed acyclic graphs (acyclic digraphs).

I had to write a random DAG generating algorithm for a JUnit test for a topological ordering algorithm and I was wondering if there is a proven theoretical minimum time complexity that can be achieved for a random DAG generating algorithm.