Despite the central role of light absorption and the subsequent generation of free charge carriers in organic and hybrid organic-inorganic photovoltaics, the precise process of this initial photoconversion is still debated. We employ a novel broadband (UV-Vis-NIR) transient absorption spectroscopy setup to probe charge generation and recombination in the thin films of the recently suggested hybrid material combination poly(3-hexylthiophene)/silicon (P3HT/Si) with 40 fs time resolution. Our approach allows for monitoring the time evolution of the relevant transient species under various excitation intensities and excitation wavelengths. Both in regioregular (RR) and regiorandom (RRa) P3HT, we observe an instant (<40 fs) creation of singlet excitons, which subsequently dissociate to form polarons in 140 fs. The quantum yield of polaron formation through dissociation of delocalized excitons is significantly enhanced by adding Si as an electron acceptor, revealing ultrafast electron transfer from P3HT to Si. P3HT/Si films with aggregated RR-P3HT are found to provide free charge carriers in planar as well as in bulk heterojunctions, and losses are due to nongeminate recombination. In contrast for RRa-P3HT/Si, geminate recombination of bound carriers is observed as the dominant loss mechanism. Site-selective excitation by variation of pump wavelength uncovers an energy transfer from P3HT coils to aggregates with a 1/e transfer time of 3 ps and reveals a factor of 2 more efficient polaron formation using aggregated RR-P3HT compared to disordered RRa-P3HT. Therefore, we find that polymer structural order rather than excess energy is the key criterion for free charge generation in hybrid P3HT/Si solar cells.