If the Higgs vacuum expectation value (VEV) in early universe is about one percent higher than its present value, the Lithium-7 puzzle in BBN and the Hubble tension between the CMB data and the late-time measurements are mitigated. We proposed a model of an ultralight axion coupled to the Higgs field, named ``axi-Higgs'', to achieve this goal (https://arxiv.org/pdf/2102.11257.pdf). The axion initial profile yields the required shift to the Higgs VEV throughout the BBN-recombination epoch and a percent-level contribution to the total matter density today. Because of its very large de Broglie wavelength, this axion suppresses the matter power spectrum, alleviating the CMB S8/sigma8 tension with the weak-lensing data. It also explains the recently reported isotropic cosmic birefringence by its coupling with photons. The model predicts that the shift to the Higgs VEV may be detected by the spectral measurements of quasars, while its oscillation may be observed in the atomic clock measurements.