This dissertation traces the evolution of cosmology from its foundational theories to the forefront of modern observational studies, with a particular focus on the role of large-scale structure (LSS) probes. It begins with the establishment of General Relativity in 1915 and the development of Friedmann's equations in the 1930s, marking the \textbf{Big Bang Moment} that laid the groundwork for modern cosmological exploration. The theoretical advancements that followed, coupled with the discovery of the expanding Universe, created the framework that underpins contemporary cosmology. The detection of the Cosmic Microwave Background (CMB) in 1965 marked the \textbf{First-Light Moment}, confirming the thermal history of the Universe and solidifying the hot Big Bang theory as the model for the early Universe.

As cosmology progressed, it entered the \textbf{Matter-Dominated Era} in the 1970s, when the existence of dark matter became widely accepted due to extensive observational evidence from galaxies. During this period, the foundational understanding of the galaxy-dark-matter relation was established. Redshift surveys and galaxies began to play a crucial role in measuring cosmological parameters, such as the amount of matter ($\Omega_m \sim 0.1$), which fuelled the debate over replacing the Einstein-de-Sitter Universe model ($\Omega_m=1$). The introduction of the $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model in 1984, bolstered by subsequent discoveries like the Universe's accelerated expansion, further advanced the field.

The \textbf{$\Lambda$-Dominated Epoch} is characterised by precise cosmological measurements from cosmic probes, including CMB anisotropies and Baryonic Acoustic Oscillations (BAO) and Redshift Space Distortions (RSD) from redshift surveys such as the Sloan Digital Sky Survey (SDSS). These measurements confirmed that the cosmological constant $\Lambda$ is the best candidate for \textit{dark energy}, the dominant energy component of the Universe today. In 2024, the Dark Energy Spectroscopic Instrument (DESI) survey published its first cosmological results, potentially signifying a new era in cosmology with the robust detection of dynamic dark energy.

I have been contributed to SDSS and DESI collaborations since 2019. During my PhD, I upgraded the SubHalo Abundance Matching (SHAM) method to empirically describe the galaxy-dark-matter-halo connection. My work led to a generalized SHAM algorithm that incorperates observational systematics and is applicable to all galaxy and quasar tracers from any redshift survey. Additionally, I modelled the spectroscopic systematics (including redshift catastrophics and redshift uncertainty) for the largest sample of DESI -- ELGs, ensuring the biases they bring to the cosmological measurements are well under control. These efforts contribute to the robustness of the cosmological measurements from SDSS and DESI.