SEO is an important consideration for any website and, if you are having a new website built, it should be taken into account from the outset. Once you start with a rebuild project, it will be too late to consider SEO as thoroughly as it should be considered, as it should inform content, site structure, URL structure, and more. It is a factor that should be discussed with a web design agency long before the actual build process takes place.
SEO and web design should really be seen as one in the same thing, with each one informing the other. They work closely together and as such, should be considered in parallel. Choosing a web design agency that also knows about SEO and search marketing will really help you to push your project in the right direction and keep it in line with SEO best practice. Any agency you work with should be well qualified in both areas.