This cannot be a 'true' zip file. The central directory is at the end of the zip file. It's made up of information that is needed for the decompression. So if you are streaming it, you cannot decompress until the entire file is reassembled.
The only wrinkle is that each entry has a header which typically states the compressed size and checksum. Either you have to compress each entry content in some temp buffer or file to figure out the compressed size and checksum, then write out the header and compressed content. Or you write out the header with these fields zeroed, then compress the content on the fly and write it out, then write out a data descriptor with the compressed size and checksum.