Stretch Storries in a Sprint should the be added at the Start or when we know we have capacity

I work in an organization that wants to maximize capacity 

That's an awful thing to want to do, and no reason at all to use Scrum. It would be smarter to maximize value, which is not the same thing. A  Scrum Master's first duty is not to appease, but to carefully manage people's understanding of such things.

This seems to be an output-centric approach. Scrum is an outcome-centered approach. The purpose of Scrum is not to do more work in less time. The purpose of Scrum is to allow the team to maximize the value delivered and quickly adapt and pivot as they and the key stakeholders learn more about what is valuable.

You shouldn't talk about a Sprint and the work in a Sprint without talking about the Product Goal and the Sprint Goal. The primary objective of the Sprint is to achieve the Sprint Goal. However, how the team handles the rest of their capacity to do work once the Sprint Goal is achieved is up to them.

First of all, previous answers are very important. Focus on value, not troughput. Outcome in stead of output.

When you've managed to get the organisation to appreciate that, if a team runs out of stories in the sprint, and the sprint goal has been achieved or will be achieved, you can let the developers pull more stories into the sprint. They could select the most valuable and manageable stories together with the product owner.

I always recommend to pull in new work if you really need to, in stead of taking on too much work and failing to meet the sprint goal or removing stories from the sprint. It makes the work more transparent, stakeholders have clear expectations and the team is happy. But if your team is self-managing and a little further in their journey, I expect them to get better in estimating how much work they can manage in a sprint, so you probably won't see this happening as much. As a scrummaster, you should facilitate that learning process.