Transient low-mass X-ray binaries (LMXBs) are usually first detected by all-sky X-ray monitors when they enter new outbursts. These detections typically occur at X-ray luminosities above ∼1036 erg/s. Observations of these sources during the early rise of the outbursts have therefore been very limited so far. However, the launch of the Einstein Probe (EP) has greatly improved our ability to detect fainter X-ray activity, unlocking access to the early rise of the outburst. In September 2024, EP detected the early onset of a new outburst from the well-known neutron star LMXB Aql X-1, catching the source at a luminosity below 1035 erg/s. We present results from a comprehensive multiwavelength campaign of this event, combining data from EP, NICER, NuSTAR, and Swift and Las Cumbres Observatory covering the full outburst from its early rise through its return to quiescence. By comparing X-ray and optical light curves obtained by the Las Cumbres Observatory during the initial rise, we show that the start of the X-ray emission lagged the optical rise by 13 days at most. We did not observe the exact moment at which the source changed from (optical or X-rays) quiescence to rise, so that other lags cannot be completely ruled out, however. Time-resolved X-ray spectroscopy revealed the evolution of the geometry and the physical properties of the accretion flow during this early stage of the outburst, as well as at higher luminosities as the source transitioned through the canonical X-ray spectral states, the hard, intermediate, and soft state. These data show that the source underwent a very rapid transition of about 12 h from the hard to the soft state about two weeks after the optical onset of the outburst. At the state transition, peculiar trends are observed for the temperature and physical sizes of the inner disk region and a blackbody near the surface of the neutron star, which might suggest that at this stage, a geometrically thicker inner disk emerges. We discuss these results in the context of timescales for outburst evolution and state transitions in accreting neutron stars and black holes.