  We propose a way to generate tiny couplings of freeze-in massive particle
dark matter with the Standard Model particles dynamically by considering an
extension of the electroweak gauge symmetry. The dark matter is considered to
be a singlet under this extended gauge symmetry which we have assumed to be the
one in a very widely studied scenario called left-right symmetric model.
Several heavy particles, that can be thermally inaccessible in the early
Universe due to their masses being greater than the reheat temperature after
inflation, can play the role of portals between dark matter and Standard Model
particles through one loop couplings. Due to the loop suppression, one can
generate the required non-thermal dark matter couplings without any need of
highly fine tuned Yukawa couplings beyond that of electron Yukawa with the
Standard Model like Higgs boson. We show that generic values of Yukawa
couplings as large as $\mathcal{O}(0.01)$ to $\mathcal{O}(1)$ can keep the dark
matter out of thermal equilibrium in the early Universe and produce the correct
relic abundance later through the freeze-in mechanism. Though the radiative
couplings of dark matter are tiny as required by the freeze-in scenario, the
associated rich particle sector of the model can be probed at ongoing and near
future experiments. The allowed values of dark matter mass can remain in a wide
range from keV to TeV order keeping the possibilities of warm and cold dark
matter equally possible.
