How do you handle content strategy for websites?

I have been doing a lot of research in handling with content strategy. I work at an agency right now and one of the biggest problems is we design first, and then add content later. Everytime the content is added, the design will change. And it will also change everytime content changes. This is pretty frustrating and I’m looking for alternatives.

I’ve heard content first as a solution to this problem but do you have other methods to deal with such problems with your clients?