  The physical scale corresponding to baryon acoustic oscillations (BAO), the
size of the sound horizon at recombination, is precisely determined by CMB
experiments. Measuring the apparent size of the BAO scale imprinted in the
clustering of galaxies gives us a direct estimate of the angular-diameter
distance and the Hubble parameter as a function of redshift. The BAO feature is
damped by non-linear structure formation, which reduces the precision with
which we can infer the BAO scale from standard galaxy clustering analysis
methods. Many methods to undo this damping via the so-called BAO reconstruction
have so far been proposed; however, they all rely on backward modeling. In this
paper, we present the first results of BAO inference from rest-frame halo
catalogs using forward modeling combined with the EFT likelihood, in the case
where the initial phases of the density field are fixed. We show that the
remaining systematic bias is less than 2% when we consider cutoff values of
$\Lambda \leq 0.25 \,h\,{\rm Mpc}^{-1}$ for all halo samples considered, and
below 1% and consistent with zero for all but the most highly biased samples.
We also demonstrate that, when compared to the standard power spectrum
likelihood approach under the same assumption of fixed phases, the 1$\sigma$
errors associated to the field level inference of the BAO scale are 1.1 to 3.3
times smaller, depending on the value of the cutoff and the halo sample. Our
analysis therefore unveils another promising feature of using field-level
inference for high-precision cosmology.
