This question is a bit tricky, given that you do not work there yet, and you are not fully aware of operational details. You want to make a suggestion based on a pain point or challenge that you know the company is having. If this information is not known to you, it might be a struggle to come up with suggestions on how things should go. To avoid sounding like a know-it-all, aim to offer areas of improvement based on information and skills you've gathered through past opportunities.
At your previous job, what made the team so efficient? What kind of improvements did you suggest? How did you establish a great working relationship with your boss? What did you do to achieve your goals and hit your targets on time? With this approach, you avoid sound condescending, and at the same time, you get to illustrate further why you're the best fit for the role. Be sure to also throw in a compliment for the company!
