A Relativistic Rocket

"Actually mankind has already built particle accelerators, where new mass is created by fast collisions." Michael

It would be more accurate to say that energy is collected from various sources, thus infinitessimally decreasing the kinetic and relativistic masses of many macro-particles and temportarily storing it as kinetic energy and relativistic mass of two very fast-moving subatomic particles---a proton and an anti-proton. When those particles collide, many new particles emerge; sometimes one of those particles may have greater rest mass than either a proton or an anti-proton. The process is ultra-inefficient; the total mass/energy of all particles involved is concerved; only the knowlege gained justifies the tremendous waste of useful energy, and the consequent accumulation of entropy on Earth.

"I wonder where in nature mass is created this way and what would be the right ingredients to form let's say a neutron (ultimatly a hydrogen atom)."

I think the majority view is that such processes haven't occurred in nature since a few seconds after the alleged "big bang". If the meta model, or some other "theory of everything", ever matures, perhaps it will provide a more palatable answer.

"...only the knowledge gained justifies the tremendous waste of useful energy, and the consequent accumulation of entropy on Earth."
You put that very nicely. That knowledge being: mass and energy can be reshuffled.

The problem with particle accelerators is that they are operated by people wearing big bang glasses. I'm sure you've heard the saying:
"When we build a bigger accelerator we can recreate circumstances very close to the beginning of the universe."
Aha. How close? All the way back to the stage where hydrogen was being formed?

Big bang and the meta model are two very different theories. The only thing we can do is observe and use common sense. And that's what we're trying to do here