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The Giotto mission was the first interplanetary probe ever flown by the European Space Agency (ESA). Selected in 1980 and flown in 1985, Giotto was the most daring of an international fleet of five spaceprobes, which triumphantly visited the comet of all comets, 1P/Halley, in March 1986. Earlier on, in 1984, ESA and NASA established a Comet Nucleus Sample Return Science Definition Team; their work led in 1993 to the selection of the Rosetta mission as the Planetary Cornerstone of ESA's long-term programme Horizon 2000. Rosetta was the first mission ever to land an automated laboratory (Philae) on the surface of a cometary nucleus and to accompany an errant body in its active phase through the Solar System. Launched in 2004, Rosetta ended its operational life on the 30th of September 2016.Giotto and Rosetta have completely transformed our understanding of comets and have contributed hugely to give Europe a well-deserved leadership in the field of cometary studies. Selecting Giotto and Rosetta, Europe demonstrated the vision and the ambition to take the lead in the worldwide effort to learn about our origins. ESA has recently selected Comet Interceptor, a much smaller-scale mission (F-class) to encounter a yet-to-be-discovered Oort cloud comet, following a novel approach to expand our horizons on a limited budget. Europe has the opportunity to confirm and reinforce this leadership with an even more daring program: AMBITION, a mission to return the firstever cryogenically-stored sample of a cometary nucleus to Earth. The international context is very favourable as, after the recent selection by NASA of the next New Frontiers class candidate mission, no international agency (NASA, CNSA, JAXA) is presently planning a sample return mission from a cometary nucleus in the next decade. NASA's New Frontiers candidate CAESAR, the unique direct competitor of AMBITION, was not selected and, even if CAESAR could still be a potential candidate for the next New Frontiers call, NASA's present timeline gives Europe a competitive edge with the AMBITION endeavour.The numerous discoveries of the Rosetta mission are of great relevance not only for their scientific significance, but also because they provided essential insight into performing critical operations and measurements. This information provides better focus for the next set of fundamental questions that can be answered by the AMBITION project. This white paper, put together by a large scientific community ranging from cosmochemists to plasma physicists, presents compelling evidence that a mission capable of returning a cryogenic sample of a cometary nucleus to be analysed on Earth, and of studying the comet both remotely and in-situ, will be able to dig deeper into our past.