  In this work we consider the realization of a variant emergent Universe
scenario in the context of $f(R)$ gravity. We use well-known reconstruction
techniques existing in the literature, and we find the approximate form of the
vacuum $f(R)$ that reproduces the specific variant emergent Universe scale
factor in the large curvature approximation. As we show, in the variant
emergent Universe scenario, the Hubble horizon shrinks primordially and the
Universe undergoes in an accelerated expansion era. In a perturbation theory
approach, the scalar and tensor curvature perturbations can be expressed in
terms of the phenomenological indices $\epsilon_i , i=1,3,4$, usually used for
inflationary phenomenology, and we extract the spectral indices for the scalar
and tensor perturbations, along with the tensor-to-scalar ratio expressed in
terms of the perturbation indices. Using a powerful genetic algorithm we
investigate in depth the parameter space of the model, quantified by several
free parameters, in order to study the viability of the model when this is
compared with the Planck 2018 data. We also investigate the implications of the
vacuum $f(R)$ gravity we found on the Big Bang nucleosynthesis.
