We present a novel UV freeze-in mechanism for enhancing the dark matter abundance in cosmologies where inflation is followed by an epoch dominated by a fluid stiffer than radiation. In such scenarios, even a small radiation abundance, produced for instance by instantaneous preheating effects, will eventually dominate the total energy density of the Universe without the need for a complete inflaton decay. For the sake of concreteness, we focus in non-oscillatory (NO) quintessential inflation models, albeit our treatment is rather general and can be extended to other scenarios. The high temperature of the initial thermal bath together with the absence of subsequent entropy injections into the Standard Model plasma translates into a highly-effective UV DM freeze-in. In particular, we find that, during kination, an enhancement in the DM abundance is generically obtained for any production cross section not-decreasing with temperature.