Encrypted traffic classification (TC) methods must adapt to new protocols and extensions as well as to advancements in other machine learning fields. In this paper, we adopt a transfer learning setup best known from computer vision. We first pretrain an embedding model on a complex task with a large number of classes and then transfer it to seven established TC datasets. The pretraining task is recognition of SNI domains in encrypted QUIC traffic, which in itself is a challenge for network monitoring due to the growing adoption of TLS Encrypted Client Hello. Our training pipeline -- featuring a disjoint class setup, ArcFace loss function, and a modern deep learning architecture -- aims to produce universal embeddings applicable across tasks. A transfer method based on model fine-tuning surpassed SOTA performance on nine of ten downstream TC tasks, with an average improvement of 6.4%. Furthermore, a comparison with a baseline method using raw packet sequences revealed unexpected findings with potential implications for the broader TC field. We released the model architecture, trained weights, and codebase for transfer learning experiments.