In typical ML you just learn the weights.
But the architecture stays fixed, and since we don't have an architecture that can realistically solve well enough all tasks, it shouldn't count as Godel machine.
Meta-learning, where you also learn hyper-parameters (including potentially the architecture) are closer to that, see for example:
- Google Vizier: https://ai.google/research/pubs/pub46180
- Microsoft neural architecture search: https://github.com/Microsoft/nni
But this is still far from a true Godel machine.