If you are loading a lot of files on your home page, such as images for a slide show, these will also have a very large impact for a user’s first visit (after which they will be cached).
Then we will look at what files you are loading and evaluate (with you) what is important and what functionality can be traded for load speed.
Depending on the site, altering the file loading sequence can make the biggest difference after caching and functionality-vs-speed trade-offs. But it is also the most work, as it means modifying and testing code. And in some cases, such as poorly designed plugins, there is nothing we can do except recommend alternatives (where they exist).
On an existing site it may not be feasible (or wanted) for us to take the last step (modifying code). But on a new or rebuilt site we will take file-loading sequence into account from the outset, as well as a number of smaller factors, such as minimizing files and avoiding external content.
For a site with a global audience, or with a lot of files to load, we may also recommend the use of a content-distribution network (CDN).
For existing websites, we can either make the necessary changes for you or simply play a consultative role, informing you what needs doing and letting you make it happen, thus avoiding any need for us to have access to your FTP account or WordPress admin. For new sites or rebuilds we will be into the code anyway and will do optimization as part of the development process.