<div><b>Context:</b> Giant planet formation in the core accretion scenario is inherently constrained by the gas disk lifetime because a massive core must form before the gas disk fully dissipates. Inspired by observations of solar system features such as the asteroid and Kuiper belts, the accretion of roughly km-sized planetesimals is traditionally considered as the main accretion mechanism of solids but such models often result in longer planet formation timescales. The accretion of mm-cm sized pebbles, on the other hand, allows for rapid core growth within the disk lifetime. The two accretion mechanisms are typically discussed separately.</div><div><br></div><div><b>Aims:</b> We investigate the interplay between the two accretion processes in a disk containing both pebbles and planetesimals for planet formation in general and in the context of giant planet formation specifically. The goal is to disentangle and understand the fundamental interactions that arise in such hybrid pebble-planetesimal models laying the groundwork for informed analysis of future, more complex, simulations.</div><div><br></div><div><b>Methods:</b> We combine a simple model of pebble formation and accretion with a global model of planet formation which considers the accretion of planetesimals. We compare synthetic populations of planets formed in disks composed of different amounts of pebbles and planetesimals to identify the impact of the combined accretion scenario. On a system-level, we study the formation pathway of giant planets in these disks.</div><div><br></div><div><b>Results:</b> We find that, in hybrid disks containing both pebbles and planetesimals, the formation of giant planets is strongly suppressed whereas in a pebbles-only or planetesimals-only scenario, giant planets can form. We identify the heating associated with the accretion of planetesimals after the pebble accretion period to delay the runaway gas accretion of massive cores. Coupled with strong inward type-I migration acting on these planets, this results in close-in icy sub-Neptunes originating from the outer disk.</div>