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When the universe undergoes a slow cosmological first-order phase transition in its early phase, the effects of cosmic expansion must be carefully evaluated. In this Letter, we perform numerical simulations of a relativistic radiation fluid to investigate how cosmic expansion during a slow FOPT alters the generation of gravitational waves. In addition to reducing bubble separations via an effectively increased nucleation rate, intriguingly, cosmic expansion induces a non-linear growth in the GW energy, ultimately leading to a significant enhancement of the gravitational waves for deflagration modes. Owing to their various way to estimate the sound wave lifetime, this enhancement is more pronounced for weak FOPTs than for intermediate FOPTs. This is contrary to previous findings, which suggested a suppression of the GW content. Our results indicate that more detailed investigations are necessary when modeling slow FOPTs.