  The TESS mission has provided a wealth of asteroseismic data for solar-like
oscillators. However, these data are subject to varying cadences, large gaps,
and unequal sampling, which complicates analysis in the frequency domain. One
solution is to model the oscillations in the time domain by treating them as
stochastically damped simple harmonic oscillators through a linear combination
of Gaussian Process kernels. We demonstrate this method on the well-studied
subgiant star nu Indi and a sample of Kepler red giant stars observed by TESS,
finding that the time domain model achieves an almost two-fold increase in
accuracy for measuring {\nu}max compared to typical frequency domain methods.
To apply the method to new detections, we use stellar parameters from Gaia DR3
and the TESS input catalog to calculate revised asteroseismic detection
probabilities for all TESS input catalog targets with T<12 mag and a predicted
{\nu}max>240{\mu}Hz. We also provide a software tool to calculate detection
probabilities for any target of interest. Using the updated detection
probabilities we show that time-domain asteroseismology is sensitive enough to
recover marginal detections, which may explain the current small number of
frequency-based detections of TESS oscillations compared to pre-flight
expectations.
