  Third-generation (3G) gravitational-wave (GW) detectors like the Einstein
Telescope (ET) will observe binary black hole (BBH) mergers at redshifts up to
$z\sim 100$. However, unequivocal determination of the origin of high-redshift
sources will remain uncertain, due to the low signal-to-noise ratio (SNR) and
poor estimate of their luminosity distance. This study proposes a machine
learning approach to infer the origins of high-redshift BBHs, specifically
differentiating those arising from Population III (Pop. III) stars - likely the
first progenitors of stellar-born BBH mergers in the Universe - and those
originated from Population I-II (Pop. I-II) stars. We have considered a wide
range of state-of-the-art models encompassing current uncertainties on Pop. III
BBH mergers. We then estimate parameter errors of detected sources with ET
using the Fisher-information-matrix formalism, followed by classification using
XGBoost, a machine learning algorithm based on decision trees. For a set of
mock observed BBHs, we provide the probability that they belong to the Pop. III
class while considering the parameter errors of each source. In our fiducial
model, we accurately identify ~10% of detected BBHs originating from Pop. III
stars with > 90% precision. Our study demonstrates how machine learning enables
to achieve some pivotal aspects of ET science case by exploring the origin of
individual high-redshift GW observations. We set the basis for further studies,
which will integrate additional simulated populations and account for
population modeling uncertainties
