I wanted to know if it's possible to do the following:
Any help would be greatly appreciated.
You could probably add a button to your thank you page via the theme editor but you would need knowledge of how Shopify themes work.
If you need it on the checkout page, Shopify recently announced Checkout app extensions which would allow you to embed functionality into the checkout page but I believe you would need to either find an existing app that works for this or you would need to build out something yourself. You can also do this apparently via Shopify scripts but this is in beta mode and only available to Shopify Plus accounts.
Do you have any suggestions on resources I could refer to on how to use the theme editor to add that button the thank you page and I'd be able to add a link to that button?
And how would I go about building something for myself if I want it on the checkout page?
I don't at the moment sorry but a quick google search for "how to customize shopify theme thank you page" should point you in the right direction.
About checkout extensions, there isn't a lot of documentation out there since it's fairly new but, in my opinion, this might be overkill since you would have to build out an app for this and all you are trying to do is add a simple button.