We present results from textsc{GigaEris}, a cosmological, $N$-body hydrodynamical ``zoom-in simulation of the formation of a Milky Way-sized galaxy with unprecedented resolution, encompassing of order a billion particles within the refined region. The simulation employs a modern implementation of smoothed-particle hydrodynamics, including metal-line cooling and metal and thermal diffusion. We focus on the early assembly of the galaxy, down to redshift $z=4.4$. The simulated galaxy has properties consistent with extrapolations of the main sequence of star-forming galaxies to higher redshifts and levels off to a star formation rate of $sim$60$, M_{odot}$yr$^{-1}$ at $z=4.4$. A compact, thin rotating stellar disk with properties analogous to those of low-redshift systems arises already at $z sim 8$-9. The galaxy rapidly develops a multi-component structure, and the disk, at least at these early stages, does not grow upside-down as often reported in the literature. Rather, at any given time, newly born stars contribute to sustain a thin disk, while the thick disk grows from stars that are primarily added through accretion and mergers. The kinematics reflect the early, ubiquitous presence of a thin disk, as a stellar disk component with $v_phi/sigma_R$ larger than unity is already present at $z sim 9$-10. Our results suggest that high-resolution spectro-photometric observations of very high-redshift galaxies should find thin rotating disks, consistent with the recent discovery of cold rotating gas disks by ALMA. Finally, we present synthetic images for the JWST NIRCam camera, showing how the early disk would be easily detectable already at $z sim 7$.
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