Antihydrogen is formed when antiprotons are mixed with cold positrons in a nested Penning trap. We present experimental evidence, obtained using our antihydrogen annihilation detector, that the spatial distribution of the emerging antihydrogen atoms is independent of the positron temperature and axially enhanced. This indicates that antihydrogen is formed before the antiprotons are in thermal equilibrium with the positron plasma. This result has important implications for the trapping and spectroscopy of antihydrogen.