An increasing number of experiments are targeting GHz bandwidth impulsive radiation induced by high energy neutrinos in ice or high energy cosmic ray air showers. Beamforming triggers improve detection prospects as effective signal-to-noise ratio scales as the square root of the number of phased array antennas in a coherent sum. However, this also brings high technological requirements with an increasing number of narrower beams required, while sub-nanosecond synchronisation must be maintained across the antennas summed in each beam. A prototype digital beamforming trigger is developed using Radio-frequency-system-on-a-chip (RFSoC), an adaptable radio platform leveraging the advantages of Field Programmable Gate Arrays (FPGAs). Findings are presented including cross channel alignment, trade-offs between resource usage and trigger efficiency and using programmable logic for flexible digital filtering capabilities.