  In standard model, the Fermi coupling constant, $G_F$, sets the strength of
electroweak decay. We attempt an approach to constrain the temporal variation
of the Fermi coupling constant $G_F$. To probe it, Type Ia supernovae (SNe Ia)
light curves are being used as a source of reliable primordial nucleosynthesis
events across the redshifts. We utilized studies suggesting that in the initial
phase after the SNe Ia explosion, the electroweak decay of $^{56}Ni \rightarrow
^{56}Co \rightarrow ^{56}Fe$ is the key contributor to powering the SNe Ia
light curve. We hence used the Pan-STARRS supernovae catalog having 1169
supernovae light curves in $g$, $r$, $i$, and $z$ spectral filters. The
post-peak decrease in the apparent magnitude of light curves (in the rest frame
of SNe) was related to the electroweak decay rate of primordial
nucleosynthesis. Further, the decay rate relates to $G_F$. To keep the analysis
independent of the cosmological model, we used the Hubble parameter measurement
and a non-parametric statistical method, the Gaussian Process. Our study
suggests a small yet finite temporal variation of $G_F$ and puts a strong upper
bound on the present value of the fractional change in the Fermi coupling
constant i.e; $\dfrac{\dot G_F}{G_F}\big\rvert_{z=0} \approx 10^{-11} yr^{-1}$
using datasets spread over a redshift range $0<z<0.75$.
