  We present a likelihood profile stacking technique based on the {\it
Fermi}-Large Area Telescope (LAT) data to explore the $\gamma$-ray
characteristics of {\it Fermi}-LAT undetected astrophysical populations. The
pipeline is applied to a sample of $\gamma$-ray unresolved extreme blazars,
i.e., sources with the highest synchrotron peak frequencies ($\nu_{\rm
Syn}^{\rm peak}\geqslant 10^{17}$ Hz), and we report a cumulative $\gamma$-ray
detection with more than 32$\sigma$ confidence for 2 degrees of freedom.
Comparing the generated stacked $\gamma$-ray spectrum with the sensitivity
limits of the upcoming Cherenkov Telescope Array (CTA), we find that the {\it
Fermi}-LAT undetected population of such extreme blazars, on average, may
remain well below the CTA detection threshold due to their faintness and
extragalactic background light (EBL) absorption. However, $\gamma$-ray detected
blazars belonging to the same class are promising candidates for CTA
observations. The EBL corrected stacked spectra of these sources do not show
any softening up to 1 TeV. This finding suggests the inverse Compton peak of
extreme blazars to lie above 1 TeV, thus indicating a hard intrinsic TeV
spectrum. Our analysis also predicts that at 100 GeV, at least $\sim$10\% of
the diffuse extragalactic $\gamma$-ray background originates from the
$\gamma$-ray undetected extreme blazars. These results highlight the
effectiveness of the developed stacking technique to explore the uncharted
territory of $\gamma$-ray undetected astrophysical objects.
