The main problem:

Firebase doesn't keep track of the child count, which we need for the randomization. We can however use DataSnapshot.numChildren().

To avoid this, you can add a count element to the /users node, which you would have to maintain manually, using cloud functions (e.g. when adding a user, increment count, and decrement on deletion).

On the other hand, since the cloud functions are on the server, and firebase will manage the cache for you, it is not a big deal to actually use DataSnapshot.numChildren(), since the data will be cached once the function has been executed for the first time, and will be updated only when there are changes.

Therefore I would recommend to utilize the numChildren() function:

db.ref('/users').once('value').then(snapshot => 
    Math.floor((Math.random() * snapshot.numChildren()))
);

Alternatively using the count-method:

db.ref('/users/count').once('value').then(snapshot => 
    Math.floor((Math.random() * snapshot.val()))
);

Getting the random Node:

db.ref('/users').orderByKey().startAt(random).limitToFirst(1);

Method 1:

// https://stackoverflow.com/a/38423694/4161937
// attach permanent listener to force firebase caching (not sure if it works for this case)
db.ref('/users').on('value', () => {});
// will read #random amount of items
db.ref('/users').orderByKey().limitToFirst(random).once('value').then(users => Object.keys(users)[random]);

Method 2:

// https://stackoverflow.com/a/38423694/4161937
// attach permanent listener to force firebase caching
db.ref('/users').on('value', () => {});
db.ref('/users').once('value').then(users => Object.keys()[random])

You can read more about query order- and filtering in the official docs:

Retrieving Data - How Data is Ordered