How do I create a customer account with inventory?

Site URL: https://www.stackstorage.ca/

My client runs a storage company (www.stackstorage.ca) where they have a list of items you can store based on size or space required. The user goes onto their site, selects what they want to put into storage (let's say golf clubs, bulky sized item, $8/month) and then when they checkout, they select a time and date that they want the item picked up--this process is already complete.

Now my client wants the user to be able to log back onto the website, see a catalog of what they've put into storage, select an item (golf clubs) and request that it be delivered back to them to go golfing. They would click on golf clubs, add to the cart, select a date & time for delivery, and be charged a flat $25 delivery fee. Once they ask for the item back, they will no longer be charged a monthly fee of $8 for storing that item.

One problem I see is that on Squarespace, it doesn't allow you to force a customer to create an account. Therefore if people don't make an account, a catalog of items doesn't exist for them.

Wondering if this is possible? I know that it will involve some code, but unsure of where to even start.