You could create the customer account, and then create & send an invoice. OR, you can send the customer a link to register an account, and then create the one-off invoice under their account. They'd get an email with the invoice, and a link to pay it.
It's not possible to create an invoice that is not attached to a pre-existing account though.
To allow a client to register, you just need to create an order form of the type "Client Registration". Packages > Order Forms > Create button. Then select "Client Registration" under "Type". Send them a link to this registration page so they can create an account, and then invoice them.