  Molecular oxygen is a strong indicator of life on Earth, and may indicate
biological processes on exoplanets too. Recent studies proposed that Earth-like
O$_\mathrm{2}$ levels might be detectable on nearby exoplanets using
high-resolution spectrographs on future extremely large telescopes (ELTs).
However, these studies did not consider constraints like relative velocities,
planet occurrence rates, and target observability. We expanded on past studies
by creating a homogeneous catalog of 286,391 main-sequence stars within 120 pc
using Gaia DR3, and used the Bioverse framework to simulate the likelihood of
finding nearby transiting Earth analogs. We also simulated a survey of M dwarfs
within 20 pc accounting for $\eta_{\oplus}$ estimates, transit probabilities,
relative velocities, and target observability to determine how long ELTs and
theoretical 50-100 meter ground-based telescopes need to observe to probe for
Earth-like O$_\mathrm{2}$ levels with an $R=100,000$ spectrograph. This would
only be possible within 50 years for up to $\sim$21% of nearby M dwarf systems
if a suitable transiting habitable zone Earth-analog was discovered, assuming
signals from every observable partial transit from each ELT can be combined. If
so, Earth-like O$_\mathrm{2}$ levels could be detectable on TRAPPIST-1 d-g
within 16 to 55 years, respectively, and about half that time with an
$R=500,000$ spectrograph. These results have important implications for whether
ELTs can survey nearby habitable zone Earth analogs for O$_\mathrm{2}$ via
transmission spectroscopy. Our work provides the most comprehensive assessment
to date of the ground-based capabilities to search for life beyond the solar
system.
