  A promising idea to resolve the long standing Hubble tension is to postulate
a new subdominant dark-energy-like component in the pre-recombination Universe
which is traditionally termed as the Early Dark Energy (EDE). However, as shown
in Refs. \cite{Hill:2020osr,Ivanov:2020ril} the cosmic microwave background
(CMB) and large-scale structure (LSS) data impose tight constraints on this
proposal. Here, we revisit these strong bounds considering the Planck CMB
temperature anisotropy data at large angular scales and the SPTPol polarization
and lensing measurements. As advocated in Ref. \cite{Chudaykin:2020acu}, this
combined data approach predicts the CMB lensing effect consistent with the
$\Lambda$CDM expectation and allows one to efficiently probe both large and
small angular scales. Combining Planck and SPTPol CMB data with the full-shape
BOSS likelihood and information from photometric LSS surveys in the EDE
analysis we found for the Hubble constant $H_0=69.79\pm0.99\,{\rm
km\,s^{-1}Mpc^{-1}}$ and for the EDE fraction $f_{\rm EDE}<0.094\,(2\sigma)$.
These bounds obtained without including a local distance ladder measurement of
$H_0$ (SH0ES) alleviate the Hubble tension to a $2.5\sigma$ level. Including
further the SH0ES data we obtain $H_0=71.81\pm1.19\,{\rm km\,s^{-1}Mpc^{-1}}$
and $f_{\rm EDE}=0.088\pm0.034$ in full accordance with SH0ES. We also found
that a higher value of $H_0$ does not significantly deteriorate the fit to the
LSS data. Overall, the EDE scenario is (though weakly) favoured over
$\Lambda$CDM even after accounting for unconstrained directions in the
cosmological parameter space. We conclude that the large-scale Planck
temperature and SPTPol polarization measurements along with LSS data do not
rule out the EDE model as a resolution of the Hubble tension. This paper
underlines the importance of the CMB lensing effect for robust constraints on
the EDE scenario.
