I'm Miles from the Social Care team at Shopify.
At this stage, we don't have a built-in option for customers to upload products. Thankfully, our wonderful Shopify Partners have come up with some really good apps that can easily integrate into your store. These apps will allow customers to upload their own designs and will be accessible through the apps once a customer has placed their order. I've recommended a couple of apps below for you.
If these apps aren't suitable, I'd recommend checking the App Store for other upload apps.
Have a great day!