We report on our ongoing project aimed at providing a precise Standard Model prediction for the hadronic vacuum polarization contribution to the muon’s anomalous magnetic moment \(a_\mu \) , from first principles using lattice QCD. There is currently a discrepancy of \(4.2\,\sigma \) between the direct measurement of \(a_\mu \) and the Standard Model prediction with the hadronic vacuum polarization contribution \(a_\mu ^\textrm{hvp}\) evaluated via the traditional data-driven approach based on hadronic cross sections. We present our calculation of the so-called window observable whose value is in tension with hadronic cross section data, which precludes a straightforward interpretation of the new experimental measurement of \(a_\mu \) . We focus on our efforts to minimize statistical noise in our calculations using deflation techniques and dedicated spectrum calculations to constrain the long-distance regime of the electromagnetic current correlator, which is a crucial step for our goal of providing a refined estimate for \(a_\mu ^\textrm{hvp}\) with total uncertainties well below the percent level.