From the screenshot it looks like you are referring to ChatGPT and GPTs in particular, not the API.
The questions are the ‘conversation starters’ and they show only for the first question.
What you can do is instruct the GPT to start a conversation by only answering one of the conversation starters (which you may need to add to the instructions separately) and then further instruct to prompt the user to select a follow up question by entering a number , like ‘1’.
This is not exactly what you are asking for, but it is something that has been implemented a lot. It allows you to guide both LLM and user to stay on a predefined path.