It's not exactly training, but Google just recently previewed a LLM with a million-token context that can do effectively the same thing. One of the tests they did was to put a dictionary for a very obscure language (only 200 speakers worldwide) into the context, knowing that nothing about that language was in its original training data, and the LLM was able to translate it fluently.

OpenAI has already said they’re not making that publicly available for now

This just means that OpenAI is voluntarily ceding the field to more ambitious companies.