The superconductivity of cuprates, which has been a mystery ever since its discovery decades ago, is created through doping electrons or holes into a Mott insulator. There, however, exists an inherent electron-hole asymmetry in cuprates. The layered crystal structures of cuprates enable collective charge excitations fundamentally different from those of three-dimensional metals, i.e., acoustic plasmons. Acoustic plasmons have been recently observed in electron-doped cuprates by resonant inelastic X-ray scattering (RIXS); in contrast, there is no evidence for acoustic plasmons in hole-doped cuprates, despite extensive measurements. This contrast led us to investigate whether the doped holes in cuprates La$_{2-x}$Sr$_x$CuO$_4$ are conducting carriers or are too incoherent to induce collective charge excitation. Here we present momentum-resolved RIXS measurements and calculations of collective charge response via the loss function to reconcile the aforementioned issues. Our results provide unprecedented spectroscopic evidence for the acoustic plasmons and long sought conducting p holes in hole-doped cuprates.