In the ultra-high dynamic and low Signal-to-Noise Ratio(SNR) communication scenarios like deep space communication, traditional signal acquisition methods suffer from inadequate dynamic range support, insufficient accuracy, and the use of a narrowband Doppler model leading to poor approximation accuracy in the received signal. A wideband Doppler model is employed to model the received signal and a chirp signal is used for Doppler estimation and timing estimation. A sampling rate adjustment method based on binary-search is proposed for the receiver to overcome the mismatch between the Doppler-stretched signal and the local signal sampling rate. The simulation results of the synchronization performance show that the proposed method using Up-Down Linear Frequency Modulation(UD-LFM) signal is capable of achieving a Doppler estimation error below 400 Hz and a timing estimation error below 60 ns under a SNR of -49 dB and a maximum Doppler frequency of 2 MHz. Compared to direct acquiring, the proposed method bears a higher acquisition accuracy and a lower SNR threshold.