git stash store "$(git stash create)"
Will create stash entry similar to what you would get with git stash without actually touching and clearing your working directory and index.
If you check stash list or look at all commit graph (including stash) you'll see that it's similar result to what you would get with normal call to git stash. Just the message in stash list is different (normally it's something like "stash@{0}: WIP on master: 14e009e init commit",  here we'll get "stash@{0}: Created via "git stash store"")
$ git status --short
M file.txt
A  file2.txt
$ git stash list
$ git stash store "$(git stash create)"
$ git stash list
stash@{0}: Created via "git stash store".
$ git stash show 'stash@{0}'
 file.txt  | 2 +-
 file2.txt | 2 ++
 2 files changed, 3 insertions(+), 1 deletion(-)
$ git log --oneline --graph --all
*   85f937b (refs/stash) WIP on master: 14e009e init commit
|\
| * 26295a3 index on master: 14e009e init commit
|/
* 14e009e (HEAD -> master) init commit
$ git status
M file.txt
A  file2.txt
A bit more explanation:
A git stash entry is represented using normal commits with some defined structure. Basically it is a regular commit object that has 2 parents (or 3 if you use --include-untracked option) (more info 1,2).
git stash create creates this commits that represents stash entry and returns you the object name (SHA-1) of commit object (the one that has 2 or 3 parents). It is a dangling commit (you can verify it by calling git fsck after git stash create).  You need to make refs/stash point to this dangling commit and you do it by git stash store (or by git update-ref like in other answers, because git stash store uses git update-ref to do its work).
It's good to look at actual source code of git stash push and see that it's basically calling git stash create and git stash store and then does some logic to clean files (which one depends on what options you used in git stash push).