  In this work, we explore the possibility that Early Dark Energy (EDE) is
dynamical in nature and study its effect on cosmological observables. We
introduce a parameterization of the equation of state allowing for an equation
of state $w$ differing considerably from cosmological constant (cc, $w={-1}$)
and vary both the initial $w_i$ as well final $w_f$ equation of state of the
EDE fluid. This idea is motivated by the fact that in many models of EDE, the
scalar field may have some kinetic energy when it starts to behave like EDE
before the CMB decoupling. We find that the present data have a mild preference
for non-cc early dark energy $( w_i= -0.78)$ using Planck+BAO+Pantheon+S$H_0$ES
data sets, leading to $\Delta \chi^2_{\rm min}$ improvement of -2.5 at the
expense of one more parameter. However, $w_i$ is only weakly constrained, with
$w_i < -0.56$ at $1\sigma$. We argue that allowing for $w_i\neq -1$ can play a
role in decreasing the $\sigma_8$ parameter. Yet, in practice the decrease is
only $\sim0.4\sigma$ and $\sigma_8$ is still larger than weak lensing
measurements. We conclude that while promising, a dynamical EDE cannot resolve
both $H_0$ and $\sigma_8$ tensions simultaneously.
