The estimation of forest above-ground biomass (AGB) can be significantly improved by leveraging remote sensing (RS) and deep learning (DL) techniques. In this process, it is crucial to obtain appropriate RS features and develop a suitable model. However, traditional methods such as random forest (RF) feature selection often fail to adequately consider the complex relationships within high-dimensional RS feature spaces. Moreover, challenges related to parameter selection and overfitting inherent in DL models may compromise the accuracy of AGB estimation. Therefore, this study proposes a novel framework based on freely available Sentinel-1 synthetic aperture radar (SAR) and Sentinel-2 optical data. Firstly, we designed new indices through the formula analogous with vegetation index calculation to integrate multidimensional spectral and structural information. Then, leveraging the simplicity of computational principles, a pigeon-inspired optimization algorithm (PIO) was introduced into a bi-directional long short-term memory neural network (PIO-BiLSTM), which achieved the set objective function through repeated iteration and validation to obtain the optimal model parameters. Finally, to verify the framework’s effect, we conducted experiments in two different tree species and compared another seven classical optimization algorithms and machine learning models. The results indicated that the new indices significantly improved the inversion accuracy of all models in both categories, and the PIO-BiLSTM model achieved the highest accuracy (Category-1: R2 = 0.8055, MAE = 8.8475 Mg·ha−1, RMSE = 12.2876 Mg·ha−1, relative RMSE = 18.1715%; Category-2: R2 = 0.7956, MAE = 1.7103 Mg·ha−1, RMSE = 2.2887 Mg·ha−1, relative RMSE = 9.3000%). Compared with existing methods, the proposed framework greatly reduced the labor costs in parameter selection, and its potential uncertainty also decreased by up to 9.0%. Furthermore, the proposed method has a strong generalization ability and is independent of tree species, indicating its great potential for future forest AGB inversion in wider regions with diverse forest types.