How can I create a database where entries are compressed files searchable by index?
Have you tested the lz6 compression level?  lz6 provides less overall compression but it has a index on values which you can pull out without going through the overhead and cost of uncompressing the whole file.  I

If you cannot give up any compression at all, have you tried a simple json document store DB such as Mongo?  I feel using filestream in SQL Server might be overkill but it depends on your environment.  It seems like you're a linux shop from the terminology used, is that correct?

I feel you can use any DBMS to store the simple values such as customerid, date, and filepath then pass the filepath over to your app.  It depends on what solutions you already have in place or which you're very comfortable with that aren't overkill.  For example, Hadoop or something complex would be crazy for this but a key value store DB might be perfect.  Maybe you can make the zip files have the customer id or something in it and only store the date (key) and path (value) in your document store.