Floquet–Bloch states are known to form in solids under periodic driving of electrons. We visualize their ultrafast build-up with angle-resolved photoemission spectroscopy and subcycle time resolution. We drive the Dirac surface state of a topological insulator with mid-infrared fields in the MV/cm range. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle. Intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics.
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