With the continuous growth of the aviation sector, concerns regarding the effects of aircraft noise on the health and well-being of communities living in the vicinity of airports have been increasing. Aircraft noise annoyance is inherently subjective and its accurate prediction and quantification represent challenging tasks. There is a lack of consensus in the scientific community regarding which metrics are the best predictors for this type of annoyance. Additionally, many of the metrics employed in the field of (psycho)acoustics are typically computationally expensive. This study aims at developing a methodology which leverages machine learning techniques for instant predictions of various sound metrics and for annoyance rating predictions from input aircraft flyover recordings. The two-step framework involves a Convolutional Neural Network (CNN) for the former, followed by artificial intelligence (AI) models which use the CNN predictions as input for the latter, such as the Support Vector Machine and Random Forest. A listening experiment was conducted in order to gather labeled annoyance data from 60 aircraft flyover recordings of both landings and take-offs and a correlation analysis was subsequently made considering a large pool of sound metrics. The results show that, in general, metrics derived from Psychoacoustic Annoyance models, especially those of Zwicker and Di et al., present better performance as predictors compared to conventional metrics and most Sound Quality Metrics taken individually. Moreover, the AI framework achieves very promising results for both the annoyance ratings and metric predictions (overall, mean absolute errors of the annoyance ratings of approximately 0.4 and below, and R2 values above 0.85), highlighting the potential for bypassing the typically long overhead associated with computing SQMs (which involve expensive and complex algorithms). The drawn conclusions are dependent on the limited amount of data that was available. Hence, the results require further validation using more recordings of various types of aircraft.