The TIMESPOT project aims at the construction of a mini-tracker demonstrator implementing both high space and time resolutions at the single pixel level. The pixels have a pitch of 55 × 55 μm2. Specified time resolution is equal or better than 50 ps. Developed sensors are based both on 3D silicon and diamond technologies, whose layout and fabrication process have been suitably optimized for best time resolution. Read-out pixel electronics is being developed in 28-nm CMOS technology. The first batch of 3D silicon sensors, containing several test structures based on different geometries of the electrodes, has been delivered in June 2019 and has been tested against its timing performance both under laser and minimum ionizing particle beams. In the present paper, the output of these starting measurements is presented. The sensors show very good timing performance, having σ¡30 ps (sigma), although operated with non-optimized front-end electronics and in noisy environment. These results represent an important step forward in the development of pixels with timing operating at extremely high interaction rates and fluences, as required in the next generation of upgraded colliders. •A crucial challenge about future vertex detectors consists in realizing pixel with timing capabilities.•In this respect, we need sensors and electronics having at the same time the following requirements: space resolutions of O(10 μm), time resolutions below 50 ps, radiation resistance ¿ 1016 1 MeV neutron equivalent per cm2.•We have developed and fabricated dedicated fast silicon sensors in 3D technology with a pitch of 55 μm.•They have been proved to have time resolutions below 30 ps.