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The processes and ranges of intensive variables that control magma transport and dyke propagation through the crust are poorly understood. Here we show that textural and compositional data of olivine crystals (Mg/Fe, Ni and P) from the tephra of the first months of Paricutin volcano monogenetic eruption (Mexico, 1943–1952) record fast growth and large temperature and oxygen fugacity gradients. We interpret that these gradients are due to convective magma transport in a propagating dyke to the Earth’s surface in less than a few days. The shortest time we have obtained is 0.1 day, and more than 50% of the calculated timescales are < 2 days for the earliest erupted tephra, which implies magma ascent rates of about 0.1 and 1 m s⁻¹. The olivine zoning patterns change with the eruptive stratigraphy, and record a transition towards a more steady magma flow before the transition from explosive to effusive dynamics. Our results can inform numerical and experimental analogue models of dyke propagation, and thus facilitate a better understanding of the seismicity and other precursors of dyke-fed eruptions.