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We use zoom-in, hydrodynamical, cosmological $N$-body simulations tracing theformation of the first stellar clumps from the SImulating the Environmentswhere Globular clusters Emerged (SIEGE) project, to study key structuralproperties of dark matter haloes when the Universe was only $0.92$ Gyr old. Thevery high-resolution (maximum physical resolution 0.3 h$^{-1}$ pc at $z=6.14$,smallest dark-matter particle mass $164\,M_{\odot}$) allows us to reach thevery low mass end of the stellar-to-halo mass relation ($M_{\rmvir}=10^{7.5-9.5}\,M_{\odot}$) to study the processes that mould dark matterhaloes during the first stages of structure formation. We investigate the roleof baryonic cooling and stellar feedback, modeled from individual stars, inshaping haloes, and of environmental effects as accretion of dark matter alongcosmic filaments and mergers. We find that the onset of star formation(typically for $\log M_{\rm vir}/M_{\odot}\simeq7.6$) causes the inner cusp inthe haloes density profile to flatten into a core with constant density andsize proportionally to the halo virial mass. Even at these mass scales, weconfirm that baryons make haloes that have formed stars rounder in the centralregions than haloes that have not formed stars yet, with median minor-to-major$\langle q \rangle$ and intermediate-to-major $\langle s \rangle$ axes 0.66 and0.84, respectively. Our morphological analysis shows that, at $z=6.14$, haloesare largely prolate in the outer parts, with the major axis aligned alongfilaments of the cosmic web or towards smaller sub-haloes, with the degree ofelongation having no significant dependence on the halo mass.

Shaping the unseen: the influence of baryons and environment on low-mass, high-redshift dark matter haloes in the SIEGE simulations