How can I see a client's cart before they check out?

[MBTallant]

My online store is going to be event decor rental. I need to see a client's cart so that I can check availability of items for each client's event date. I am trying to figure out a way for a client to "check out" but not pay yet because the items may not be available for their event date. I can send an invoice with the contract attached. By sending an invoice, it will also allow me to charge half as a deposit and set up the last payment before pick-up. Any suggestions on how to make this work?

[alexandriak]

I don't use the square website BUT thought I could offer some suggestions

If square has an abandoned cart feature you could possibly look and see that way. Just make sure the customer gets almost thru the checkout process so you'd have a name. 

Install something on your website that records visitors while they're on there (but obviously doesn't record CC info entered)