This thesis investigates the relationship between galaxy observables and the large-scale structure to extract information on the initial conditions of the universe. The origin of the late-time cosmic acceleration is one of the most persisting questions in modern cosmology. In order to address it, various probes have been exploited, all suffering from observational and modeling uncertainties. Through its formation history, the large-scale structure contains information on the initial conditions of the universe. As a result, the relation between observables and the large-scale structure must be understood to obtain an accurate picture of our universe.

The thesis describes two novel field-level approaches to study supernova and galaxy environments. In the former, we show that supernovae trace the large-scale structure similarly to galaxies. This suggests that supernovae can be used as tracers of cosmic structure, particularly where survey magnitude limitations provide only sparse galaxy samples. In the latter, we present a 4σ detection of galaxy intrinsic alignment, namely the correlation of galaxy shapes with the large-scale gravitational tidal field. I conclude by summarizing two studies in progress; A framework of constraining photometric galaxy redshifts with the large-scale structure and a novel joint inference of three-dimensional peculiar velocities constrained with galaxy clustering and type Ia supernovae as standard candles. The findings of my research shed new light on field-level studies of cosmic environments through galaxy clustering. This opens the possibility for the understanding of the relationship between observables and the large-scale structure at galaxy scales and the future development of multiprobe cosmological frameworks.