It has recently been shown that a subdominant hidden sector of atomic dark matter in the early universe can resolve the Hubble tension while maintaining good agreement with most precision cosmological observables. However, such a solution requires a hidden sector whose energy density ratios are the same as in our sector and whose recombination also takes place at redshift $z approx 1100$, which presents an apparent fine tuning. We introduce a realistic model of this scenario that dynamically enforces these coincidences without fine tuning. In our setup, the hidden sector contains an identical copy of Standard Model (SM) fields, but has a smaller Higgs vacuum expectation value (VEV) and a lower temperature. The baryon asymmetries and reheat temperatures in both sectors arise from the decays of an Affleck-Dine scalar field, whose branching ratios automatically ensure that the reheat temperature in each sector is proportional to the corresponding Higgs VEV. The same setup also naturally ensures that the Hydrogen binding energy in each sector is proportional to the corresponding VEV, so the ratios of binding energy to temperature are approximately equal in the two sectors. Furthermore, our scenario predicts a correlation between the SM/hidden temperature ratio and the atomic dark matter abundance and automatically yields values for these quantities that resolve the Hubble tension.
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