In this talk, I will present a model that simultaneously addresses the doublet-triplet splitting problem of grand unified theories, the electroweak hierarchy problem, and the strong CP problem. The mechanism relies on the dynamics of two axion-like particles and on cosmological selection around the QCD phase transition: the universe would crunch if the triplets were light or developed a vacuum expectation value, or if the doublets were heavy or failed to develop one. As a result, the cosmological evolution selects vacua with the desired Higgs structure. The low-energy remnant of the mechanism is a pair of axion-like particles weakly coupled to the Standard Model, which could be probed in upcoming axion experiments or through a combination of neutron EDM measurements and astrophysical signatures of fuzzy dark matter.