We characterized the single-photon timing response function of various silicon photomultipliers (SiPMs) over a broad (500-1100 nm) spectral range. We selected two SiPM manufacturers, and we investigated two active areas, i.e., a small (1-1.69 mm2 and a large (9 mm2) one, for each of them. We demonstrate that selected SiPMs are suitable for time-resolved diffuse optics (DO) applications where a very large detection area and sensitivity down to single photons are crucial to detecting the very faint return signal from biological tissues, like the brain, thus allowing replacement of photomultiplier tubes and opening the way to a novel generation of DO multichannel instrumentation. Due to our custom front-end electronics, we show the world's bes...