  In any cosmological model where spacetime is described by a pseudo-Riemannian
manifold, photons propagate along null geodesics, and their number is
conserved, upcoming Gravitational Wave (GW) observations can be combined with
measurements of the Baryon Acoustic Oscillation (BAO) angular scale to provide
model-independent estimates of the sound horizon at the baryon-drag epoch. By
focusing on the accuracy expected from forthcoming surveys such as LISA GW
standard sirens and DESI or Euclid angular BAO measurements, we forecast a
relative precision of $\sigma_{r_{\rm d}} /r_{\rm d} \sim 1.5\%$ within the
redshift range $z \lesssim 1$. This approach will offer a unique
model-independent measure of a fundamental scale characterizing the early
universe, which is competitive with model-dependent values inferred within
specific theoretical frameworks. These measurements can serve as a consistency
test for $\Lambda$CDM, potentially clarifying the nature of the Hubble tension
and confirming or ruling out new physics prior to recombination with a
statistical significance of $\sim 4\sigma$.
