This paper considers the non pilot data-aided estimation of the carrier frequency offset (CFO) and sample frequency offset (SFO) of orthogonal frequency division multiplexing (OFDM) signals in fast time-varying channel. The main obstacle is the time-variant channel response, which deteriorates the estimation validity. A practical approach to mitigate this impact is to reduce the time consumption of one-shot estimation. In this way, we propose a method to reduce the time consumption to within one OFDM symbol duration. The maximum likelihood (ML) estimator is derived based on the observations of frequency domain constellations output of two FFTs on one symbol; its closed-form approximation is then derived to reduce the calculation burden. Remarkably, our method does not require any training symbol or pilot tone embedded in the signal spectrum, therefore achieves the highest spectral efficiency. Theoretical analysis and simulation results are employed to assess the performance of proposed method in comparison with existing alternatives.