Madsen founds Rocket Madsen Space Lab (RML), a non-profit organization dedicated to amateur rocketry and manned spaceflight. RML becomes a prominent platform for his ambitions to build and launch rockets independently.

Madsen, along with Kristian von Bengtson, co-founds Copenhagen Suborbitals, an open-source space program aiming to send a human into space on a suborbital flight. The project gains international attention and attracts volunteers and funding. Internal conflicts and disagreements with von Bengtson lead to Madsen's departure from Copenhagen Suborbitals in 2014.

Following his departure from Copenhagen Suborbitals, Madsen establishes Rocket Factory ApS. He focuses his efforts on constructing the UC3 Nautilus, a privately-built submarine. Simultaneously, he continues to pursue rocketry projects, albeit with less public visibility than before.