Siteground will already have optimised web servers. Your site is relatively large and probably needs some tinkering around, this is the responsibility you have to take when you host it yourself. https://tools.pingdom.com will be a good tool to work out how to increase performance.

Some tips:

Look at the assets being delivered and if they are optimized. Is your clients site sending down full scale images that are larger then they get displayed on the site.

Bigger is not always better here.

JS/CSS are you sending all rules with comments, spacing and tabbing when just the rules will do. Are your rules repeating themselves and being moot.

make sure the site is ready for production, and is not a development version expecting the hosting server to do all the work to make you site fast.

That should be done in the build stage.

Grunt and gulp are your friends!