How can I take orders without taking payment?

I want customers to put their items in the basket and be able to send their order to me without using checkout  ( we are preparing an invoice mannualy).  Is it possible?

No unfortunately, it is not possible. Squarespace requires payment upfront. The only thing i could suggest trying is applying an automatic 100% discount so that they are not charged from your square space site. that way Squarespace receives its mandatory payment and you get your order. Otherwise maybe try out a quote based system using contact forms? 

Same here! I would love to be able to do this!

I too would love to do that. We make clothing for kids and adults with disabilities, and often get customers paying with vouchers from disability societies.

Maybe leave the site in test mode??

https://support.squarespace.com/hc/en-us/articles/205811368-Running-test-orders

What about making an "Events" page instead and make your products events where you can then direct people to fill out an order form?