  In the present work, we describe the results obtained with a large ($\approx
133$ cm$^3$) TeO$_2$ bolometer, with a view to a search for neutrinoless
double-beta decay ($0\nu\beta\beta$) of $^{130}$Te. We demonstrate an efficient
$\alpha$ particle discrimination (99.9\%) with a high acceptance of the
$0\nu\beta\beta$ signal (about 96\%), expected at $\approx 2.5$ MeV. This
unprecedented result was possible thanks to the superior performance (10 eV rms
baseline noise) of a Neganov-Luke-assisted germanium bolometer used to detect a
tiny (70 eV) light signal from the TeO$_2$ detector, dominated by
$\gamma$($\beta$)-induced Cherenkov radiation but exhibiting also a clear
scintillation component. The obtained results represent a major breakthrough
towards the TeO$_2$-based version of CUORE Upgrade with Particle IDentification
(CUPID), a ton-scale cryogenic $0\nu\beta\beta$ experiment proposed as a
follow-up to the CUORE project with particle identification. The CUORE
experiment began recently a search for neutrinoless double-beta decay of
$^{130}$Te with an array of 988 125-cm$^3$ TeO$_2$ bolometers. The lack of
$\alpha$ discrimination in CUORE makes $\alpha$ decays at the detector surface
the dominant background component, at the level of $\approx 0.01$ counts/(keV
kg y) in the region of interest. We show here, for the first time with a
CUORE-size bolometer and using the same technology as CUORE for the readout of
both heat and light signals, that surface $\alpha$ background can be fully
rejected.
