Cosmic inflation, in which the early universe undergoes a short, violent expansion, has successfully described many phenomena, including the near scale-invariance of the Cosmic Microwave Background Radiation (CMB). However, inflation is not ultraviolet-complete and suffers from self-consistency issues. Holographic Cosmology is an alternative framework in which the early universe is described by a three-dimensional dual quantum field theory (QFT). Correlations in the CMB are predicted by two-point correlators of the energy-momentum tensor (EMT) of the dual theory. A perturbative treatment of holographic cosmology has proven competitive with inflation in fits to CMB data, however, a non-perturbative treatment is needed to test the theory against all multipoles of the CMB. Lattice QFT provides such an approach by regularizing theories through placing them on a finite spacetime lattice. In this thesis, we tackle three challenges in making predictions of holographic cosmology using a lattice-regulated dual QFT with scalar fields in the adjoint of SU(N) and a �4 interaction. First, we provide numerical evidence supporting a conjecture that a class of super-renormalizable theories, including holographic cosmology dual theories, is non-perturbatively infrared finite. This is necessary for holographic cosmology to be predictive and implies a resolution of the Big Bang singularity within the holographic cosmology framework. Secondly, we explore a novel approach to regulating ultraviolet divergences appearing in calculations of the two-point EMT correlator. In this approach, Laplace transforms of position-space lattice data offer cancellation of quadratic divergences appearing in momentum-space. We finally investigate the feasibility of using multilevel methods to reduce statistical noise in holographic dual two-point calculations. Holographic dualities necessitate correlator calculations to be done in the critical regime where the correlation length diverges. Through a novel study of the critical-scaling properties of the multilevel algorithm, using the 2D-Ising model, we demonstrate the unsuitability of the technique in this regime.