We present a re-analysis of cosmic shear and galaxy clustering from first-year Dark Energy Survey data (DES Y1), making use of a Hybrid Effective Field Theory (HEFT) approach to model the galaxy-matter relation on weakly non-linear scales, initially proposed in Modi et al. (2020) (arXiv:1910.07097). This allows us to explore the enhancement in cosmological constraining power enabled by extending the galaxy clustering scale range typically used in projected large-scale structure analyses. Our analysis is based on a recomputed harmonic-space data vector and covariance matrix, carefully accounting for all sources of mode-coupling, non-Gaussianity and shot noise, which allows us to provide robust goodness-of-fit measures. We use the textsc{AbacusSummit} suite of simulations to build an emulator for the HEFT model predictions. We find that this model can explain the galaxy clustering and shear data up to wavenumbers $k_{rm max}sim 0.6, {rm Mpc}^{-1}$. We constrain $(S_8,Omega_m) = (0.786pm 0.020,0.273^{+0.030}_{-0.036})$ at the fiducial $k_{rm max}sim 0.3, {rm Mpc}^{-1}$, improving to $(S_8,Omega_m) = (0.786^{+0.015}_{-0.018},0.266^{+0.024}_{-0.027})$ at $k_{rm max}sim 0.5, {rm Mpc}^{-1}$. This represents a $sim10%$ and $sim35%$ improvement on the constraints derived respectively on both parameters using a linear bias relation on a reduced scale range ($k_{rm max}lesssim0.15,{rm Mpc}^{-1}$), in spite of the 15 additional parameters involved in the HEFT model. We investigate whether HEFT can be used to constrain the Hubble parameter and find $H_0= 70.7_{-3.5}^{+3.0},{rm km},s^{-1},{rm Mpc}^{-1}$. Our constraints are investigative and subject to certain caveats discussed in the text.
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