Indeed : both dark matter and dark energy come both at the same time out of the big bang, exploded from the Big Crunch Singularity of a former universe. ( Q.FFF Theory) . see image of the splitting black hole singularity black hole BIG BANG.
The splitted dark matter singularity made multiple Axion based smaller black holes. Each also evaporating into the local Axion Dark Enery vacuum (image below) So; The Black Hole splinters also evaporated into new oscillating Axion vacuum particles.
But they also created new fermions at the new Penrose "Trapped Space horizon"acting as a particle collider.
Conclusion: Dark energy vacuum particles and Dark matter Whimps, (variable Axion splinter black holes) both, seem to be produced by the Big Bang explosion and Axion evaporation.