This thesis investigates transport coefficients in relativistic heavy-ion collisions using a hybrid approach. Relativistic heavy-ion collisions recreate extreme conditions of temperature and density, enabling the study of the quark-gluon plasma and the QCD phase diagram. To describe the full dynamical evolution, the SMASH-vHLLE hybrid model is employed, combining hadronic transport for the non-equilibrium initial and late stages with viscous hydrodynamics for the dense intermediate stage. A key focus is the determination of shear and bulk viscosities, η/s and ζ/s, as functions of temperature and baryochemical potential. The sensitivity of final-state observables to different initial state models (IP-Glasma, TRENTo, SMASH) is analyzed, demonstrating that initial transverse momentum distributions strongly influence flow anisotropies. To constrain transport coefficients, Bayesian inference is applied, combining experimental data with model predictions in a statistically consistent framework. Results indicate a strong temperature dependence of shear viscosity, vanishing near the crossover temperature, and substantial bulk viscosity values. The baryon-density dependence of shear viscosity remains less constrained, highlighting the need for more experimental data at finite μB. This work represents the first Bayesian extraction of temperature- and density-dependent viscosities in hybrid models with hadronic initial states. The findings improve our understanding of QCD matter under extreme conditions and have implications for future experiments at FAIR and astrophysical studies of neutron stars.