Automatic traffic classification is increasingly important in networking due to the current trend of encrypting transport information (e.g., behind HTTP encrypted tunnels) which prevent intermediate nodes to access end-to-end transport headers. This paper proposes an architecture for supporting Quality of Service (QoS) in hybrid terrestrial and SATCOM networks based on automated traffic classification. Traffic profiles are constructed by machine-learning (ML) algorithms using the series of packet sizes and arrival times of QUIC connections. Thus, the proposed QoS method does not require explicit setup of a path (i.e. it provides soft QoS), but employs agents within the network to verify that flows conform to a given traffic profile. Results over a range of ML models encourage integrating ML technology in SATCOM equipment. The availability of higher computation power at low-cost creates the fertile ground for implementation of these techniques.