When detonated on the Earth's surface, large explosions emit distinctive acoustic signatures that propagate over vast distances with relatively low attenuation in the form of infrasound. Infrasound stations hundreds of kilometers from the impulsive source can record the propagated pressure signal, atmospheric conditions permitting. Here, we present a method to estimate the explosion yield from regional infrasound signals using synthetic data and machine learning (ML). We first generate full-waveform regional infrasound with source-receiver distances between 20 and 500 km using scaled-yield source models, realistic atmospheric specifications, and normal-mode wave propagation. The use of synthetic data circumvents the paucity and sometimes sensitive nature of explosion-related infrasonic data. Extracted ML features from the waveform, point of origin, and propagation effects are then fed into a random forest regressor that estimates the yield of the source between 1 and 1,500 tonnes of equivalent TNT. When applied to five surface shots from the Humming Roadrunner (HRR) experiment, our method performs reasonably well and compares favorably with other methods despite not being trained on real data. By leveraging broadband propagation techniques with machine learning, we seek to enhance the effectiveness and applicability of explosion monitoring and build on the growing trend of deep learning applications within the seismoacoustic community.