To fully capitalize on the potential and versatility of resonant inelastic x-ray scattering (RIXS), it is essential to develop the capability to interpret different RIXS contributions through calculations, including the dependence on momentum transfer, from first principles for correlated materials. Toward that objective, we present new methodology for calculating the full RIXS response of a correlated metal in an unbiased fashion. Through comparison of measurements and calculations that tune the incident photon energy over a wide portion of the Fe L3 absorption resonance of the benchmark material BaFe2 As2 , we show that the RIXS response in BaFe2 As2 is dominated by the direct-channel contribution, including the Raman-like response below threshold. Calculations are initially performed within the first-principles Bethe-Salpeter equation (BSE) framework, which we then significantly improve by invoking a quasiboson model to describe the secondary excitations within the intermediate state. This enhancement allows the many-electron RIXS signal to be approximated as a convolution of BSE-calculated spectra with effective spectral functions. We construct these spectral functions, also from first principles, by employing the cumulant expansion of the Green's function and performing a real-time time-dependent density functional theory calculation of the response of the electronic system to the perturbation of the intermediate-state excitation. Importantly, this process allows us to evaluate the indirect RIXS response from first principles, accounting for the full periodicity of the crystal structure and with full dependence on the momentum transfer.