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SrTiO3 is known for its proximity to a ferroelectric phase and for showing an 'optimal' doping for superconductivity with a characteristic dome-like behaviour resembling systems close to a quantum critical point. Several mechanisms have been proposed to link these phenomena, but the abundance of undetermined parameters prevents a definite assessment. Here, we use ab initio computations supplemented with a microscopic model to study the linear coupling between conduction electrons and the ferroelectric soft transverse modes allowed in the presence of spin-orbit coupling. We find a robust Rashba-like coupling, which can become surprisingly strong for particular forms of the polar eigenvector. We characterize this sensitivity for general eigenvectors and, for the particular form deduced by hyper-Raman scattering experiments, we find a BCS pairing coupling constant of the right order of magnitude to support superconductivity. The ab initio computations enable us to go beyond the linear-in-momentum conventional Rashba-like interaction and naturally explain the dome behaviour including a characteristic asymmetry. The dome is attributed to a momentum dependent quenching of the angular momentum due to a competition between spin-orbit and hopping energies. The optimum density for having maximum Tc results in rather good agreement with experiments without free parameters. These results make the generalized Rashba dynamic coupling to the ferroelectric soft mode a compelling pairing mechanism to understand bulk superconductivity in doped SrTiO3.