Photocrosslinking of hydrogels with non-pulsed red light offers improved biocompatibility and deep tissue penetration in contrast to traditional UV-initiated methods. However, hydrogels fabricated upon red-light excitation are always colored by a photoinitiator, limiting their use in applications requiring high optical transparency, such as (bio)sensors, ophthalmological applications, or wound dressings. Additionally, the cytotoxicity of a photoinitiator is always a concern, especially in bioapplications. Herein, a photoinitiating system composed of an FDA-approved methylene blue photosensitizer and cytocompatible triethanolamine is introduced. The system can induce photopolymerization upon 625 nm irradiation and leaves no visible trace of the methylene blue color afterward, thus named "traceless". With this approach, gelatine methacrylate hydrogel is successfully polymerized under ambient conditions. The hydrogel is permanently colorless with well-controlled stiffness due to the light-dependent nature of the polymerization process. The system is further successfully applied in extrusion-based 3D-bioprinting with NIH-3T3 fibroblasts, followed by photocuring to produce cell-laden 3D structures, indicating its potential for tissue engineering. Upon culturing the cell-laden constructs, the fibroblasts are able to proliferate and adhere to the hydrogel material. The red-light excitation enables polymerization through at least 5 mm of biological tissue, projecting, inter alia, its use for transdermal photopolymerization in minimally invasive implantation.