Autism Spectrum Disorder (ASD) is a neurodevelopmental condition that occurs across the life cycle and affects verbal and behavioral social interaction and communication capabilities. Based on the limitation of current methodologies, this paper introduces a work that introduces a facial image-based screening system to screen early ASD using a combination of deep and machine learning techniques. Of the data used, 6,018 children's facial images with an age range of 2 to 12 years were used and standard preprocessing such as resizing, normalization, and augmentation was undertaken to enhance the data and model's overfitting resistance. Extraction of features from a range of deep architectures such as EfficientNetB0, B3, B4, DenseNet121, InceptionV3, and ResNet50 was the critical operation in the process. Both the combination of ResNet50 and DenseNet121 was undertaken with the aim to merge the residual and densely connected architectures of the two models to their fullest potential and extract both facial and fine-grained facial features. The resulting face feature vectors were then used to classify the images using various customized Fully Connected Network (FCN) classifiers. Out of the varied FCNs considered in the research, the model with the combination of the feature extractor and the model with the combination of the two models in its FCN layer and the use of batch normalization, activity regularization, learning rate decay, and dropout achieved the highest performance with 96.29 % accuracy. Experimental results affirm the new hybrid approach to have the potential to be a non-invasive, accurate, and effective way to support the early screening of ASD from facial image recognition and also possibly complement conventional approaches and make early autism detection more readily available