Elliptical galaxies today appear aligned with the large-scale structure of the Universe, but it is still an open question when they acquire this alignment. Observational data is currently insufficient to provide constraints on the time evolution of intrinsic alignments, and hence existing models range from assuming that galaxies gain some primordial alignment at formation, to suggesting that they react instantaneously to tidal interactions with the large-scale structure. Using the cosmological hydrodynamical simulation Horizon-AGN, we measure the relative alignments between the major axes of galaxies and eigenvectors of the tidal field as a function of redshift. We focus on constraining the time evolution of the alignment of the main progenitors of massive $z=0$ elliptical galaxies, the main weak lensing contaminant at low redshift. We show that this population, which at $z=0$ has a stellar mass above $10^{10.4}$ M$_odot$, transitions from having no alignment with the tidal field at $z=3$, to a significant alignment by $z=1$. From $z=0.5$ they preserve their alignment at an approximately constant level until $z=0$. We find a mass-dependence of the alignment signal of elliptical progenitors, whereby ellipticals that are less massive today ($10^{10.4}<M/{rm M}_odot<10^{10.7}$) do not become aligned till later redshifts ($z<2$), compared to more massive counterparts. We also present an extended study of progenitor alignments in the parameter space of stellar mass and galaxy dynamics, the impact of shape definition and tidal field smoothing.
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