Sign language (SL) plays a significant part in communication among people who are hearing and deaf. Silent people struggle to convey their message to others. Since most people have not received a formal language education, it is highly complex to transfer messages in an emergency. Hence, a solution to this problem is to convert SL into a human voice. Gesture-to-speech systems usually use either vision-based or non-vision-based technologies, such as cameras or wearable sensors. However, many existing solutions lack cost-effectiveness and flexibility; for example, some depend on specific hardware or only function in controlled environments. In this paper, the Advancing Sign Language Accessibility using Deep Learning-Based Hand Gesture Recognition (ASLA-DLHGR) technique for hearing and speech-impaired individuals is proposed. The goal of the ASLA-DLHGR technique is to recognize hand gestures for communication among disabled people. Initially, the data pre-processing process is performed using the bilateral filtering (BF) model. Furthermore, the ASLA-DLHGR technique employs the SqueezeNet model to learn composite features from the pre-processed data. Moreover, the tunicate swarm algorithm (TSA) based hyperparameter process is performed to enhance the performance of the SqueezeNet method. For the gesture recognition process, a hybrid of a convolutional neural network and a bidirectional long short-term memory (CNN-BiLSTM) method is implemented. To demonstrate the managed gesture recognition proficiency of the ASLA-DLHGR method, a comprehensive comparative study is carried out under the American SL dataset. The comparison study of the ASLA-DLHGR method portrayed a superior accuracy value of 99.98% over existing models.