It is possible to create a splash page otuside of WordPress, but this will only handle the home-page loadings, so when people click through to another section/page it will most likely still have the same loading issues if people are still going to the inner pages the same way.
The key to this is the same as every other type of debugging. You have to work in stages and work through the areas that could be wrong in order to find where the issue is. First step is to look at the database logs and slow queries to see what issues are there. From there look at the server running the database itself, then look at the connection between the database server and the web server. After that check the web servers logs.
Seeing as how you’re a database analyist, then you should be able to trouble-shoot the database itself without any issues. The rest might need the help of a sys-admin to get the details out of the server logs.