  Inspired by the recent conjecture originated from graduated dark energy that
the Universe has recently transitioned from anti-de Sitter vacua to de Sitter
vacua, we extend the $\Lambda$CDM model by a cosmological constant
($\Lambda_{\rm s}$) that switches sign at a certain redshift $z_\dagger$, and
we call this model $\Lambda_{\rm s}$CDM. We discuss the construction and
theoretical features of this model and find out that, when the consistency of
$\Lambda_{\rm s}$CDM with the CMB data is ensured, (i) $z_\dagger\gtrsim1.1$ is
implied by the condition that the Universe monotonically expands, (ii) $H_0$
and $M_B$ (type Ia supernovae absolute magnitude) values are inversely
correlated with $z_\dagger$ and reach $H_0\approx74.5~{\rm km\, s^{-1}\,
Mpc^{-1}}$ and $M_B\approx-19.2\,{\rm mag}$ for $z_\dagger=1.5$, in agreement
with the SH0ES measurements, and (iii) $H(z)$ presents an excellent fit to the
Ly-$\alpha$ measurements provided that $z_\dagger\lesssim 2.34$. We further
investigate the model constraints by using the full Planck CMB data set, with
and without BAO data. We find that the CMB data alone does not constrain
$z_\dagger$, but the CMB+BAO data set favors the sign switch of $\Lambda_{\rm
s}$ providing the constraint: $z_\dagger=2.44\pm0.29$ (68% C.L.). Our analysis
reveals that the lower and upper limits of $z_\dagger$ are controlled by the
Galaxy and Ly-$\alpha$ BAO measurements, respectively, and the larger
$z_{\dagger}$ values imposed by the Galaxy BAO data prevent the model from
achieving the highest local $H_0$ measurements. In general, $\Lambda_{\rm
s}$CDM (i) relaxes the $H_0$ tension while being fully consistent with the TRGB
measurements, (ii) relaxes the $M_B$ tension, (iii) removes the discrepancy
with the Ly-$\alpha$ measurements, (iv) relaxes the $S_8$ tension, and (v)
finds a better agreement with the BBN constraints on the physical baryon
density. [Abridged]
