When reddit started out and had almost no user base, they had employees each impersonate a handful of different users to give the site a sense of a pre-existing community. When Dwarf Fortress was starting out, their sole developer would create custom ASCII-art scenes to send to every supporter above a certain dollar threshold.
It is counterintuitive at first but when you think about it actually makes a lot of sense. When you're getting started you should focus on doing things to get started. Worry about scaling when you're scaling.
You can work on automating it and hooking various payment providers.
Integration with payment providers is a lot of hassle and engineering work. So when you have 5-10 customers it does not make sense to automate that.
Sending invoices manually does not scale of course - but that advice is given in specific context of company. Where you should focus on working on your product and not on automating invoices "because somewhere in the future it will be needed."