Precise Point Positioning (PPP) enables an absolute positioning with centimeter-level accuracy without the need of raw measurements from a reference station. However, today's GPS L1/ L2-based PPP solutions typically need more than 30 minutes to converge. In this paper, we present a PPP solution with a much faster convergence using the proposed next-generation GNSS Kepler. We exploit the high accuracy of the satellite position, clock offset and bias estimates enabled by highly accurate optical inter-satellite range measurements. We additionally exploit the low noise level of the E1, E5 and E6 pseudorange measurements based on wideband signals as provided already by Galileo. Our PPP solution determines the receiver position and clock offset, tropospheric and ionospheric zenith delays, and pseudorange multipath errors without the need of any prior information. We show that the PPP convergence time can be reduced from more than 30 minutes to less than 5 minutes with Kepler.