  The ability of Big Bang Nucleosynthesis theory to accurately predict the
primordial abundances of helium and deuterium, as well as the baryon content of
the Universe, is considered one of the most significant achievements in modern
physics. In the present study, we consider two highly motivated hybrid $f(T)$
models and constrain them using the observations from the Big Bang
Nucleosynthesis era. In addition, using late-time observations of Cosmic
Chronometers and Gamma-Ray-Bursts, the ranges of the model parameters are
confined which are in good agreement with early time bounds. Subsequently, the
common ranges obtained from the analysis for early and late time are
summarized. Further, we verify the intermediating epochs by investigating the
profiles of cosmographic parameters using the model parameter values from the
common range. From this study, we find the considered teleparallel models are
viable candidates to explain the primordial-intermediating-present epochs.
