The initial conditions for targeted energy transfer in coupled nonlinear oscillators are investigated. First it is shown that optimal targeted energy transfer and complete energy exchange in non-conservative systems are basically the same in the system of a linear oscillator coupled with a nonlinear energy sink. An assumption and an inference are proposed that there is a proportional relationship between initial energy for inducing optimal targeted energy transfer and the cubic stiffness based on the research of slow-flow dynamics of the non-conservative system. The assumption and inference are verified by numerical simulations. The result can be applied for design of the cubic stiffness for inducing optimal targeted energy transfer in the system of a linear oscillator coupled with a nonlinear energy sink, and the method is also given in the paper.