  In this paper, we discuss the Bianchi type-I cosmological model in the
framework of symmetric teleparallel gravity say $f(Q)$ gravity in which the
non-metricity term $Q$ is responsible for the gravitational interaction. We
consider a special form of the $f\left( Q\right) $ function which can be cast
as $f\left( Q\right) =\lambda Q^{n}$, where $\lambda $ and $n$ both are the
dynamical model parameters. Such a choice can be viewed as a hybrid scale
factor that leads to a relation between cosmic time and redshift as $% t=\left(
\frac{\alpha t_{0}}{\beta }\right) W\left[ \frac{\beta }{\alpha }e^{%
\frac{\beta -\ln \left( 1+z\right) }{\alpha }}\right] $ which describes a $%
\Lambda $CDM model of the Universe with the expansion evolving from
decelerating to an acceleration phase. The best values for the model parameters
i.e. $\alpha $ and $\beta $ that would accord with the most current
observational datasets are then estimated. We make use of 57 points from the
Hubble dataset, 1048 points from the supernovae of type Ia dataset and 6 points
from the BAO dataset. We use the Markov Chain Monte Carlo (MCMC) technique in
conjunction with Bayesian analysis and the likelihood function. Further, we
study the validity of our model with the investigation of the thermodynamical
quantities, energy conditions along with some physical variables such as the
EoS, and jerk parameters. Next, our results are discussed in light of current
observational data and trends.

General Relativity and Quantum Cosmology