  The redshifted 21-cm signal from the Cosmic Dawn and Epoch of Reionization
carries invaluable information about the cosmology and astrophysics of the
early Universe. Analyzing the data from a sky-averaged 21-cm signal experiment
typically involves navigating through an intricate parameter space to
accurately address various factors such as foregrounds, beam uncertainties,
ionospheric distortions, and receiver noise for the search of the cosmological
21-cm signal. The traditional likelihood-based sampling methods for modeling
these effects could become computationally demanding for such highly complex
models, which makes it infeasible to include physically motivated 21-cm signal
models in the analysis. Moreover, the inference with these traditional methods
is driven by the assumed functional form of the likelihood function. This work
demonstrates how Simulation-Based Inference through Truncated Marginal Neural
Ratio Estimation (TMNRE) can naturally handle these issues at a significantly
reduced computational cost than the likelihood-based methods. We estimate the
posterior distribution on our model parameters with TMNRE for simulated mock
observations, composed of beam-weighted foregrounds, physically motivated 21-cm
signal, and radiometric noise. We find that maximizing the information content
by simultaneously analyzing the data from multiple time slices and antennas
significantly improves the parameter constraints and leads to a better
exploration of the cosmological signal. We discuss the application of TMNRE for
the current configuration of the REACH experiment and demonstrate how it can be
utilized to explore potential avenues for REACH. The method presented here can
be easily generalized for any sky-averaged 21-cm signal experiment.
