Recently, an intriguing research trend for automatic target recognition (ATR) from synthetic aperture radar (SAR) imagery has arisen: using simulated data to train ATR models is a feasible solution to the issue of inadequate measured data. To close the domain gap that exists between the real and simulated data, the unsupervised domain adaptation (UDA) techniques are frequently exploited to construct ATR models. However, for UDA, the target domain lacks labeled data to direct the model training, posing a great challenge to ATR performance. To address the above problem, a semi-supervised domain adaptation (SSDA) framework has been proposed adopting progressive multi-level alignments for simulated data-aided SAR ATR. First, a progressive wavelet transform data augmentation (PWTDA) is presented by analyzing the discrepancies of wavelet decomposition sub-bands of two domain images, obtaining the domain-level alignment. Specifically, the domain gap is narrowed by mixing the wavelet transform high-frequency sub-band components. Second, we develop an asymptotic instance-prototype alignment (AIPA) strategy to push the source domain instances close to the corresponding target prototypes, aiming to achieve category-level alignment. Moreover, the consistency alignment is implemented by excavating the strong-weak augmentation consistency of both individual samples and the multi-sample relationship, enhancing the generalization capability of the model. Extensive experiments on the Synthetic and Measured Paired Labeled Experiment (SAMPLE) dataset, indicate that our approach obtains recognition accuracies of 99.63% and 98.91% in two common experimental settings with only one labeled sample per class of the target domain, outperforming the most advanced SSDA techniques.