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ABSTRACT Theoretical arguments and observations suggest that in massive haloes ($$>10^{12}\, {\rm M}_\odot$$), the circumgalactic medium (CGM) is dominated by a ‘hot’ phase with gas temperature near the virial temperature ($$T\approx T_{\rm vir}$$) and a quasi-hydrostatic pressure profile. Lower-mass haloes are however unlikely to be filled with a similar quasi-static hot phase, due to rapid radiative cooling. Using the FIRE (Feedback In Realistic Environment) cosmological zoom simulations, we demonstrate that the hot phase is indeed subdominant at inner radii ($$\lesssim 0.3 R_{\rm vir}$$) of $$\lesssim 10^{12}\, {\rm M}_\odot$$ haloes, and the inner CGM is instead filled with $$T\ll T_{\rm vir}$$ gas originating in outflows and inflows, with a turbulent velocity comparable to the halo virial velocity. The turbulent velocity thus exceeds the mass-weighted sound speed in the inner CGM, and the turbulence is supersonic. UV absorption features from such CGM trace the wide lognormal density distributions of the predominantly cool and turbulent volume-filling phase, in contrast with tracing localized cool ‘clouds’ embedded in a hot medium. We predict equivalent widths of $$W_\lambda \sim 2\lambda v_{\rm c}/c\sim 1$$Å for a broad range of strong UV and EUV transitions (Mg ii, C ii, C iv, Si ii–iv, O iii–v) in sightlines through inner CGM dominated by turbulent pressure of $$\lesssim L^\star$$ galaxies at redshifts $$0\le z\lesssim 2$$, where $$\lambda$$ is the transition wavelength, $$v_{\rm c}$$ is the circular velocity, and c is the speed of light. Comparison of our predictions with observational constraints suggests that star forming $$\lesssim$$ $$L^\star$$ and dwarf galaxies are generally dominated by turbulent pressure in their inner CGM, rather than by thermal pressure. The inner CGM surrounding these galaxies is thus qualitatively distinct from that around quenched galaxies and massive discs such as the Milky-Way and M31, in which thermal pressure likely dominates.