Current research in the field of positron emission tomography (PET) focuses on improving the sensitivity of the scanner with thicker detectors, extended axial field-of-view, and time-of-flight (TOF) capability. These create the need for depth-of-interaction (DOI) encoding to correct parallax errors. We have proposed a method to encode DOI using phosphor-coated crystals. Our initial work using photomultiplier tubes (PMTs) demonstrated the possibilities of the proposed method, however, a major limitation of PMTs for this application is poor quantum efficiency in yellow light, corresponding to the wavelengths of the converted light by the phosphor coating. In contrast, the red-green-blue-high-density (RGB-HD) silicon photomultipliers (SiPMs) have a high photon detection efficiency across the visible spectrum. Excellent coincidence resolving time (CRT; ) was obtained by coupling RGB-HD SiPMs and lutetium fine silicate crystals coated on a third of one of their lateral sides. Events were classified in three DOI bins ( width) with an average sensitivity of 83.1%. A CRT of combined with robust DOI encoding is a marked improvement in the phosphor-coated approach that we pioneered. For the first time, we read out these crystals with SiPMs and clearly demonstrated the potential of the RGB-HD SiPMs for this TOF-DOI PET detector.