The redshifted 21 cm transition line of hydrogen tracks the thermal evolution of the neutral intergalactic medium (IGM) at cosmic dawn, during the emergence of the first luminous astrophysical objects (~100 Myr after the Big Bang) but before these objects ionized the IGM (~400-800 Myr after the Big Bang). Because X-rays, in particular, are likely to be the chief energy courier for heating the IGM, measurements of the 21 cm signature can be used to infer knowledge about the first astrophysical X-ray sources. Using analytic arguments and a numerical population synthesis algorithm, we argue that the progenitors of supermassive black holes (SMBHs) should be the dominant source of hard astrophysical X-rays---and thus the primary driver of IGM heating and the 21 cm signature---at redshifts $z < 20$, if (i) they grow readily from the remnants of Population III stars and (ii) produce X-rays in quantities comparable to what is observed from active galactic nuclei and high-mass X-ray binaries. We show that models satisfying these assumptions dominate over contributions to IGM heating from stellar populations, and cause the 21 cm brightness temperature to rise at $z > 20$. An absence of such a signature in the forthcoming observational data would imply that SMBH formation occurred later (e.g. via so-called direct collapse scenarios), that it was not a common occurrence in early galaxies and protogalaxies, or that it produced far fewer X-rays than empirical trends at lower redshifts, either due to intrinsic dimness (radiative inefficiency) or Compton-thick obscuration close to the source.
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