When can a bakers apprentice invent new pastries?

On or off company time??

You can experiment at any time.

Baking is a very exacting science so you would have to have learned the chemistry of baking various items before you could start experimenting with any hopes of success.

@SQUEEKY2 On company time.

That would very much depend on the relationship you’ve established with the chef. But typically, creative input from apprentices wouldn’t be well received. In a classic European bakery, an apprentice does little more than prep recipes and scrape sheet pans. Bakeries tend to operate on narrow margins, so few chefs would want to see ingredients risked on uneducated guesses.

^^He’s the expert here.

You have to be a 33rd degree High Chief before you can experiment with pastries. To do so before then is risky, as one should not meddle with forces one does not fully understand.