Early Dark Energy (EDE) contributing a fraction $f_{rm EDE}(z_c)sim 10 %$ of the energy density of the universe around $z_csimeq 3500$ and diluting as or faster than radiation afterwards, can provide a resolution to the Hubble tension, the $sim 5sigma$ discrepancy between the $H_0$ value derived from early- and late-universe observations within $Lambda$CDM. However, it has been pointed out that Large-Scale Structure (LSS) data, which are in $sim3sigma$ tension with $Lambda$CDM and EDE cosmologies, might alter these conclusions. We reassess the viability of the EDE against a host of high- and low-redshift measurements, by combining LSS observations from recent weak lensing (WL) surveys with CMB, Baryon Acoustic Oscillation (BAO), growth function (FS) and Supernova Ia (SNIa) data. Introducing a model whose only parameter is $f_{rm EDE}(z_c)$, we report a $sim 2sigma$ preference for non-zero $f_{rm EDE}(z_c)$ from Planck data alone and the tension with SH0ES is reduced below $2sigma$. Adding BAO, FS and SNIa does not affect this result, while the inclusion of a prior on $H_0$ from SH0ES increase the preference for non-zero EDE to $sim3.6sigma$. After checking the EDE non-linear matter power spectrum predicted by standard semi-analytical algorithms via a set of $N$-body simulations, we show that current WL data do not rule out EDE. We also caution against the interpretation of constraints obtained from combining statistically inconsistent data sets within the $Lambda$CDM cosmology. In light of the CMB lensing anomalies, we show that the lensing-marginalized CMB data also favor non-zero $f_{rm EDE}(z_c)$ at $sim2sigma$, predicts $H_0$ in $1.4sigma$ agreement with SH0ES and $S_8$ in $1.5sigma$ ($0.8sigma$) agreement with KV (DES) data. Alternatively, we discuss promising extensions of the EDE cosmology that could allow to fully restore cosmological concordance.
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