Assuming you know the structure of the file, you might be able to update just part of the Blob by using Blocks.
You can modify an existing block blob by inserting, replacing, or deleting existing blocks. After uploading the block or blocks that have changed, you can commit a new version of the blob by committing the new blocks with the existing blocks you want to keep using a single commit operation.
More information: Understanding Block Blobs, Append Blobs, and Page Blobs - About Block Blobs
Partially off-topic:
Looking at your scenario and the requirements, it feels like you might have picked the wrong storage type since the current one doesn't support what you're trying to do.
Also, you might want to split the 'huge' file into separate ones.