Before you ask for the bigger role, make the small one impossible to take away from you.

Trust for a bigger job is built out of evidence from the current one. Anyone deciding whether to give you more is not really assessing potential, they are asking whether the thing you already hold runs well without their attention. Ambition that arrives before that evidence reads as impatience.

Spend a few weeks making your current responsibilities dull to supervise: nothing late, nothing dropped, nothing requiring a reminder. Then ask, and point at that record rather than at how much you want it. Being obviously reliable in a small role is the most persuasive argument available.