  Topological insulators represent a new class of quantum phase defined by
invariant symmetries and spin-orbit coupling that guarantees metallic Dirac
excitations at its surface. The discoveries of these states have sparked the
hope of realizing nontrivial excitations and novel effects such as a
magnetoelectric effect and topological Majorana excitations. Here we develop a
theoretical formalism to show that a three dimensional topological insulator
can be designed artificially via stacking bilayers of two-dimensional Fermi
gases with opposite Rashba-type spin-orbit coupling on adjacent layers, and
with inter-layer quantum tunneling. We demonstrate that in the stack of
bilayers grown along a (001)-direction, a nontrivial topological phase
transition occurs above a critical number of Rashba-bilayers. In the
topological phase we find the formation of a single spin-polarized Dirac cone
at the $\Gamma$-point. This approach offers an accessible way to design
artificial topological insulators in a set up that takes full advantage of the
atomic layer deposition approach. This design principle is tunable and also
allows us to bypass limitations imposed by bulk crystal geometry.
