Fast radio burst (FRB) 190608 was detected by the Australian Square Kilometre Array Pathfinder (ASKAP) and localized to a spiral galaxy at zhost=0.11778 in the Sloan Digital Sky Survey (SDSS) footprint. The burst has a large dispersion measure (DMFRB=339.8, pc, cm-3) compared to the expected cosmic average at its redshift. It also has a large rotation measure (RMFRB=353 rad, m-2) and scattering timescale (τ = 3.3 ms at 1.28 GHz). Chittidi et al. perform a detailed analysis of the ultraviolet and optical emission of the host galaxy and estimate the host DM contribution to be 110 ± 37, pc, cm-3. This work complements theirs and reports the analysis of the optical data of galaxies in the foreground of FRB 190608 in order to explore their contributions to the FRB signal. Together, the two studies delineate an observationally driven, end-to-end study of matter distribution along an FRB sightline, the first study of its kind. Combining our Keck Cosmic Web Imager (KCWI) observations and public SDSS data, we estimate the expected cosmic dispersion measure DMcosmic along the sightline to FRB 190608. We first estimate the contribution of hot, ionized gas in intervening virialized halos (DMhalos7 28, pc, cm-3). Then, using the Monte Carlo Physarum Machine methodology, we produce a 3D map of ionized gas in cosmic web filaments and compute the DM contribution from matter outside halos (DMIGM ≈ 91-126, pc, cm-3). This implies that a greater fraction of ionized gas along this sightline is extant outside virialized halos. We also investigate whether the intervening halos can account for the large FRB rotation measure and pulse width and conclude that it is implausible. Both the pulse broadening and the large Faraday rotation likely arise from the progenitor environment or the host galaxy.