We propose and numerically demonstrate a scheme for generating isolated attosecond soft X-ray pulses based on an enhanced self-amplified spontaneous emission (ESASE) configuration that employs a non-dispersive inverse Cherenkov radiation dielectric laser accelerator (ICR-DLA) as the energy modulator. Unlike conventional modulators, whose dispersive resonance conditions distort few-cycle laser pulses, the ICR-DLA operates with a phase-matching condition strictly independent of the driving laser wavelength, thereby faithfully mapping the temporal waveform of the few-cycle pulse onto the longitudinal phase space of the electron beam. Start-to-end simulations show that a 2.5 GeV electron beam with a current of 3 kA and a normalized emittance of 0.43 mm mrad, modulated by a 4 µm few-cycle laser pulse and subsequently compressed, generates a localized density profile comprising a few discrete microbunches. The dominant central spike attains a peak current of 12.1 kA and a duration of 1.5 fs, and drives a nearly isolated soft X-ray pulse with a peak power of 10 GW and a FWHM duration of 530 as, while the adjacent satellite pulses are suppressed to below 2 GW. By overcoming the fundamental bandwidth limitations of traditional modulators, this ICR-DLA-driven scheme provides a compact and robust path toward next-generation attosecond X-ray free-electron lasers.