This study explores model-independent constraints on the universe's kinematics up to the snap and jerk hierarchical terms using the latest Baryon Acoustic Oscillation (BAO) data from the DESI collaboration. The research focuses on the cosmographic series, which includes parameters such as the deceleration $ q_0 $, jerk $ j_0 $, and snap $ s_0 $. By employing Monte Carlo Markov chain analyses, the study places stringent constraints on these parameters, showing that they are well-constrained at the $ 2\sigma $ level. The results indicate a significant departure in $ j_0 $ even at the $ 1\sigma $ confidence level, although $ q_0 $ and $ s_0 $ remain compatible with the $ \Lambda $CDM paradigm at the $ 2\sigma $ level. The $ h_0 $ tension is also alleviated in the second hierarchy, which includes the snap parameter. The study compares the results with $ \Lambda $CDM, wCDM, and Chevallier-Polarski-Linder (CPL) models, favoring the wCDM scenario. The findings demonstrate that dynamical dark energy better fits the BAO data, with the $ \Lambda $CDM model showing severe departures, particularly in $ j_0 $. The study also highlights the importance of further data to resolve tensions in $ j_0 $ and $ q_0 $. The results suggest that the $ \Lambda $CDM model is still the best fit for the overall dynamics, despite the observed deviations in certain parameters. The study concludes that the cosmographic approach provides valuable insights into the universe's kinematics without relying on a specific cosmological model.This study explores model-independent constraints on the universe's kinematics up to the snap and jerk hierarchical terms using the latest Baryon Acoustic Oscillation (BAO) data from the DESI collaboration. The research focuses on the cosmographic series, which includes parameters such as the deceleration $ q_0 $, jerk $ j_0 $, and snap $ s_0 $. By employing Monte Carlo Markov chain analyses, the study places stringent constraints on these parameters, showing that they are well-constrained at the $ 2\sigma $ level. The results indicate a significant departure in $ j_0 $ even at the $ 1\sigma $ confidence level, although $ q_0 $ and $ s_0 $ remain compatible with the $ \Lambda $CDM paradigm at the $ 2\sigma $ level. The $ h_0 $ tension is also alleviated in the second hierarchy, which includes the snap parameter. The study compares the results with $ \Lambda $CDM, wCDM, and Chevallier-Polarski-Linder (CPL) models, favoring the wCDM scenario. The findings demonstrate that dynamical dark energy better fits the BAO data, with the $ \Lambda $CDM model showing severe departures, particularly in $ j_0 $. The study also highlights the importance of further data to resolve tensions in $ j_0 $ and $ q_0 $. The results suggest that the $ \Lambda $CDM model is still the best fit for the overall dynamics, despite the observed deviations in certain parameters. The study concludes that the cosmographic approach provides valuable insights into the universe's kinematics without relying on a specific cosmological model.