PrairieSchoolCoffee

I add a little piece to this workaround, I use this for cash on delivery or bank transfer orders. If you have an accounting service, 0$ orders could be a problem.
For that, I've created some custom SKUs named, for example, "Cash on Delivery Payment" and on my accounting software (mine is a Google Sheet) I've added a rule in order to get the real price from -(discount amount).

I have requested this feature from Squarespace months ago. I'm quite surprised that manual order creation (as well as creating gift cards!) isn't a feature here when it's a feature in most e-commerce platforms.
Like @flatlander - I get around this by creating a 100% discount code + a free shipping code and ordering on behalf of my customer (who has already prepaid -- I would have sent them a Paypal invoice to complete their purchase). I use their email address so they will receive an order confirmation receipt.
@PrairieSchoolCoffee - with a 100% discount, you will not need to enter credit card info. You will simply enter the code when asked for credit card info and it will zero out the total. The order will go through without charges.

My solution to adding non-web orders to Squarespace is to create a 100% discount code. Then create the order myself on the website, checking out using code.
Hope that helps someone.