  The present epoch of the Gaia success gives us a possibility to predict the
dynamical evolution of our Solar System in the global Galactic framework with
high precision. We statistically investigated the total interaction of globular
clusters with the Solar System during six billion years of look-back time. We
estimated the gravitational influence of globular clusters' flyby onto the Oort
cloud system. To perform the realistic orbital dynamical evolution for each
individual cluster, we used our own high-order parallel dynamical $N$ body
$\varphi$-GPU code that we developed. To reconstruct the orbital trajectories
of clusters, we used five external dynamical time variable galactic potentials
selected from the IllustrisTNG-100 cosmological database and one static
potential. To detect a cluster's close passages near the Solar System, we
adopted a simple distance criterion of below 200 pc. To take into account a
cluster's measurement errors (based on Gaia DR3), we generated 1000 initial
positions and velocity randomizations for each cluster in each potential. We
found 35 globular clusters that have had close passages near the Sun in all the
six potentials during the whole lifetime of the Solar System. We can conclude
that at a relative distance of 50 pc between a GC and the SolS, we obtain on
average $\sim 15$\% of the close passage probability over all six billion
years, and at $dR=100$ pc, we get on average $\sim 35$\% of the close passage
probability over all six billion years. The globular clusters BH_140, UKS_1,
and Djorg_1 have a mean minimum relative distance to the Sun of 9, 19, and 17
pc, respectively. We can assume that a globular cluster with close passages
near the Sun is not a frequent occurrence but also not an exceptional event in
the Solar System's lifetime.
