  We study the possibility of measuring the optical depth at reionization,
$\tau$, without relying on large-scale Cosmic Microwave Background (CMB)
polarization. Our analysis is driven by the need to obtain competitive
measurements that can validate the state-of-the-art constraints on this
parameter, widely based on E-mode polarization measurements at $\ell\le 30$.
This need is partially motivated by the typical concerns regarding anomalies
observed in the Planck large-scale CMB data as well as by the remarkable fact
that, excluding these latter, $\tau$ consistently exhibits correlations with
anomalous parameters, such as $A_{\rm lens}$ and $\Omega_k$, suggesting that
slightly higher values of the optical depth at reionization could significantly
alleviate or even eliminate anomalies. Within the $\Lambda$CDM model, our most
constraining result is $\tau = 0.080 \pm 0.012$, obtained by combining Planck
temperature and polarization data at $\ell > 30$, the Atacama Cosmology
Telescope (ACT) and Planck measurements of the lensing potential, Baryon
Acoustic Oscillations (BAO), and Type-Ia supernova data from the Pantheon+
catalogue. Notably, using only ACT temperature, polarization, and lensing data
in combination with BAO and supernovae, we obtain $\tau = 0.076 \pm 0.015$,
which is entirely independent of Planck. The relative precision of these
results is approaching the constraints based on large-scale CMB polarization
($\tau = 0.054 \pm 0.008$). Despite the overall agreement, we report a slight
$1.8\sigma$ shift towards larger values of $\tau$. We also test how these
results change by extending the cosmological model. While in many extensions
they remain robust, in general obtaining precise measurements of $\tau$ may
become significantly more challenging.
