An important step for photonic quantum technologies is the demonstration of a quantum advantage through boson sampling. In order to prevent classical simulability of boson sampling, the photons need to be almost perfectly identical and almost without losses. These two requirements are connected through spectral filtering: improving one leads to a decrease of the other. A proven method of generating single photons is spontaneous parametric down-conversion (SPDC). We explore the fundamental limits of several important SPDC sources and show that an optimal tradeoff between indistinguishability and losses can always be found. We conclude that a 50-photon scattershot boson-sampling experiment using SPDC sources is possible from a computational complexity point of view. To this end, we numerically optimize SPDC sources under the regime of weak pumping and with a single spatial mode.