Hi @CharlieL and @hershyH! Thank you for joining the conversation 
I must clarify one point regarding my scenario. The invoices in my HubSpot account come from an integration with QuickBooks (QBO). This integration also uses HubSpot’s “CRM Card” functionality to work.
Keeping this in mind, I just received this reply from the support:
"There currently is no functionality available to get invoices through our API directly. The reason is the CRM Card invoice function uses a third-party’s API and webhooks to pull the data into HubSpot. The data isn’t actually stored within HubSpot.
In the case of the QBO invoice CRM Card the invoice we link to is pulled directly from QBO (the source of the invoice file/record) and not stored in HubSpot. You could use QBO’s API to GET the invoice by ID. The team have heard this feedback and is aware this is a customer painpoint."
Hope this will help you too!