If a user has already uploaded some pictures using Filestack, is it possible to offer those pictures in the picker together with the other upload options?

One way to achieve this would be to use S3 Custom Source. If you have S3 configured as your storage solution and then use the same settings under S3 Source in your developer portal, then users will see previously uploaded files in the dialog under the custom source service. This is a very basic integration without any file filtering.

If the user has an assigned ID and if you are placing their files in a specific path in your S3 bucket or in a separate bucket altogether, you can additionally include the customSourcePath parameter or the customSourceContainer parameter when the picker is launched in order to display just their files in the custom S3 source

Another alternative would be to load the picker into your own custom iframe using the container parameter, and in one section show previously uploaded files, and in another section display the standard picker options.