Use the : prefix to access objects in the current index (staged but not yet commited).
git show :file
See gitrevisions (which uses the term ‘stage 0’ for the “normal” index contents):
:[<n>:]<path>, e.g. :0:README, :READMEA colon, optionally followed by a stage number (0 to 3) and a colon, followed by a path, names a blob object in the index at the given path. A missing stage number (and the colon that follows it) names a stage 0 entry. During a merge, stage 1 is the common ancestor, stage 2 is the target branch’s version (typically the current branch), and stage 3 is the version from the branch which is being merged.