We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of ↑- and ↓-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the ↑-spins to a third spin state, which does not interact with the ↑- and ↓-spins. The resulting FFLO state has exactly one unpaired ↓-spin in each domain wall and is stable for all values of domain-wall separation and interaction strength. We show that the protocol can be implemented with high fidelity at sufficiently strong interactions for a wide range of parameters available in present-day experimental conditions. ©2017 American Physical Society.