Hello Tim,
This is easy if you know how Shopify Theme Code works but if you don’t, you have to hire a Shopify developer to do this.
Depending on the theme, it’s as simple as saying if you are on homepage template, then hide the cart drawer.
This way, the cart will be hidden from home page but will show this on other pages.
If you want you can still hide the cart from all pages with a css property called display: none;
If you want me to do this for you, please give me your store access or just DM and we can take it from there.