It is generally accepted that the four major (Galilean) satellites formed out of the gas disk that accompanied Jupiter's formation. However, understanding the specifics of the formation process is challenging as both small particles (pebbles) as well as the satellites are subject to fast migration processes. Here, we hypothesize a new scenario for the origin of the Galilean system, based on the capture of several planetesimal seeds and subsequent slow accretion of pebbles. To halt migration, we invoke an inner disk truncation radius, and other parameters are tuned for the model to match physical, dynamical, compositional, and structural constraints. In our scenario it is natural that Ganymede's mass is determined by pebble isolation. Our slow-pebble-accretion scenario then reproduces the following characteristics: (1) the mass of all the Galilean satellites; (2) the orbits of Io, Europa, and Ganymede captured in mutual 2:1 mean motion resonances; (3) the ice mass fractions of all the Galilean satellites; (4) the unique ice-rock partially differentiated Callisto and the complete differentiation of the other satellites. Our scenario is unique to simultaneously reproduce these disparate properties.