We investigate the high-redshift (z ≥ 10) Universe i.e. when it was < 1 Gyr old. We focus our investigation in two main areas: the distribution of dark matter (DM) halos and the formation of intermediate-mass (M ∼ 103 − 105 M⊙) black holes (IMBHs). We examine the abundance of DM halos as a function of redshift and mass using N-body simulations. We also analyse the influence of both Lyman-Werner (LW) radiation and metal enrichment on the number density of IMBHs using analytic models and by post-processing simulation data. We first review the state of the field today by discussing the fundamentals of Λ-Cold Dark Matter (ΛCDM), DM clustering on both small and large scales, quasars and the supermassive black holes (SMBHs) that power them. We also detail how data from the James Webb Space Telescope (JWST) have prompted us to question the origins of SMBHs and have shown us how different the high-z Universe is from the local one (z ∼ 0). Finally, we describe the computational tools employed in our investigations. Next we use the adaptive mesh-refinement code Enzo and the N-body smoothed particle hydrodynamics code SWIFT to compare (semi-)analytic DM halo mass functions against the results of direct N-body models at high redshift. Our goal is to investigate if these fitting functions could be a source of error when comparing JWST data to cosmological models. Next we compare the number density of IMBHs informed by an analytic model accounting for LW radiation and metal pollution with one informed by simulation results from Renaissance. This is a high-resolution simulation suite with the purpose of probing the high-z Universe. Our goal is to determine if recent JWST observations could be accounted for by this heavy seed formation pathway alone. We also compare this channel against other recent models in the literature. Finally, we summarise our aims, methodology, conclusions and we briefly discuss how this work could be expanded upon in future. In §2, we find that the difference between direct N-body calculations and (semi-)analytic halo mass function fits is generally < a factor of 2 (at z ∼ 10) within the mass range of galaxies currently being observed by JWST, and is therefore not a dominant source of error when comparing theory and observation at high redshift. In §3, we find the highest number densities (nheavy seed host ∼ 10−4 comoving Mpc−3 at z ∼ 10) are still too low for this channel to be the dominant formation pathway for heavy seeds when compared to JWST observations, especially when considering the growth requirements and duty cycle of active galactic nuclei (AGNs) necessary. This channel can at best be responsible for only a small subset of high-z AGNs while other models from the literature (e.g. rapid assembly) are more promising to explain JWST observations at high redshift.