  The conventional Big Bang model successfully anticipates the initial
abundances of 2H(D), 3He, and 4He, aligning remarkably well with observational
data. However, a persistent challenge arises in the case of 7Li, where the
predicted abundance exceeds observations by a factor of approximately three.
Despite numerous efforts employing traditional nuclear physics to address this
incongruity over the years, the enigma surrounding the lithium anomaly endures.
In this context, we embark on an exploration of Big Bang nucleosynthesis (BBN)
of light element abundances with the application of Tsallis non-extensive
statistics. A comparison is made between the outcomes obtained by varying the
non-extensive parameter q away from its unity value and both observational data
and abundance predictions derived from the conventional big bang model. A good
agreement is found for the abundances of 4He, 3He and 7Li, implying that the
lithium abundance puzzle might be due to a subtle fine-tuning of the physics
ingredients used to determine the BBN. However, the deuterium abundance
deviates from observations.
