An order/order confirmation is not always created from a quote before invoicing. Since an order does not always need to be created before the invoice is issued, an invoice can be generated directly from the quote.
In order to create the invoice, you can open the desired quote and select the basic action "Create invoice" on the right-hand side. Please note that the quote must have the status "Confirmed", otherwise the status action is not visible.
Clicking on "Create invoice" brings up a box where you can select which positions are transferred to the invoice. Clicking on "Save" creates the desired invoice.
The quote is then issued as a predecessor document (as is the case when creating the invoice from the order) and is also visible in the document flow for the invoice. The invoice is of course also visible in the document flow for the quote.
Furthermore, here are the various status actions of an unconfirmed quote and a confirmed quote.
Consult the report "Create a project from a quote" for information on how to create a project from a quote.