  Current inferences of the BAO scale from galaxy clustering employ a
reconstruction technique at fixed cosmology and bias parameters. Here, we
present the first consistent joint Bayesian inference of the isotropic BAO
scale, jointly varying the initial conditions as well as all bias coefficients,
based on the EFT-based field-level forward model $\texttt{LEFTfield}$. We apply
this analysis to mock data generated with a much higher cutoff (resolution),
resulting in a significant model mismatch between mock data and the model used
in the inference. We demonstrate that the remaining systematic bias in the BAO
scale is below 2% for all data considered and below 1% when Eulerian bias is
used for inference. Furthermore, we find that the inferred error on the BAO
scale is up to 1.6 times smaller compared to that from a replication of the
standard power-spectrum reconstruction approach, using the same scales as in
the field-level inference, with the improvement growing towards smaller scales
(higher $k$). Thus, a field-level approach to BAO not only allows for a
consistent inference of the BAO scale, but promises to achieve more precise
measurements on the same data as well.
