How can I populate a stream with a value from a future?

I'm using streams to monitor changes in my firestore backend. That works all right for updates, but I do not get the initial value.

class A {
  final Stream<DocumentSnapshot> _visitorCount =
      Firestore.instance.document('ServerData/serverStatus').snapshots();

  Stream<int> get visitorCount {
    return Observable(_visitorCount)
        .map((DocumentSnapshot doc) => doc['activeUsers'] as int);
  }
}

I could use rxdart's startWith to provide an initial value, but reading out this value results in a Future<int> and I'd need to supply an int to startWith.

static Future<int> f = Firestore.instance
  .collection('ServerData')
  .document('serverStatus')
  .get()
  .then((doc) => doc['activeUsers'] as int);

down the road I use it like this:

StreamBuilder(
          stream: _visitorCount,
          initialData: 0,
          builder: (context, snapshot) =>
              Text('${snapshot.data} users logged in') ...

I provide 0 as initial value but this is of course just a temporary value. I'm sure this is so obvious but still I struggle to get it right. What's the best way to solve this?

Turns out the problem I needed to solve did not require me to add some value from a future into the stream to make up for missed values. All I needed is to use a BehaviorSubject as pointed out by Remi Rousselet. But for completeness: here is how you take a value from a Future and push it into a stream:

Inserting a value from a Future into a stream

class A {
  Subject<int> _stateSubject;
  Subject<int> _state;
  Subject<int> get state {
    return _state;
  }

  A() {
    _stateSubject = new BehaviorSubject();
    _state = _stateSubject;

    Firestore.instance
        .document('ServerData/serverStatus')
        .snapshots()
        .map((DocumentSnapshot doc) => doc['activeUsers'] as int)
        .listen((int value) {
      _stateSubject.add(value);
    });
  }

  Future<int> get visitorCount => Firestore.instance
      .document('ServerData/serverStatus')
      .get()
      .then((DocumentSnapshot d) => d.data['activeUsers']);
  void addFromFuture() => visitorCount.then((int v) => _state.add(v + 1));
}

By calling addFromFuture I can query some value that will result in a Future<int>, take this value and push it into the Subject with the add() function. All the listeners to the _state-Subject will receive those updates.

Why is using a BehaviorSubject easier?

As an explanation why BehaviorSubject saves us from using this awkward workaround with Futures (taken from the RxJava docs):

Even though another subscriber came in late, the most recent received item is buffered and delivered correctly.