  The fundamental nature and origin of dark energy are one of the premier
mysteries of theoretical physics. In General Relativity Theory, the
cosmological constant $\Lambda$ is the simplest explanation for dark energy. On
the other hand, the cosmological constant $\Lambda$ suffers from a delicate
issue so-called fine-tuning problem. This motivates one to modify the spacetime
geometry of Einstein's GR. The $f(Q)$ gravity is a recently proposed modified
theory of gravity in which the non-metricity scalar $Q$ drives the
gravitational interaction. In this article, we consider a linear $f(Q)$ model,
specifically $f(Q)=\alpha Q + \beta$, where $\alpha$ and $\beta$ are free
parameters. Then we estimate the best fit values of model parameters that would
be in agreement with the recent observational data sets. We use 57 points of
the updated $H(z)$ data sets, 6 points of the BAO data sets, and 1048 points
from the Pantheon supernovae samples. We apply the Bayesian analysis and
likelihood function along with the Markov Chain Monte Carlo (MCMC) method.
Further, we analyse the physical behaviour of cosmological parameters such as
density, deceleration, and the EoS parameters corresponding to the constraint
values of the model parameters. The evolution of deceleration parameter
predicts a transition from decelerated to accelerated phases of the universe.
Further, the evolution of equation of state parameter depicts quintessence type
behaviour of the dark energy fluid part. We found that our $f(Q)$ cosmological
model can effectively describe the late time cosmic acceleration without
invoking any dark energy component in the matter part.
