Yes, you can get the orientation change earlier using WidgetsBindingObserver by overriding didChangeMetrics.

How to use didChangeMetrics

You can simply mixin WidgetBindingObserver in a State implementation of a stateful widget:

class _FooState extends State with WidgetsBindingObserver {
  @override
  void didChangeMetrics() {
    // This will be triggered by changes in orientation.
  }

  @override
  void initState() {
    super.initState();
    WidgetsBinding.instance.addObserver(this);
  }

  @override
  void dispose() {
    WidgetsBinding.instance.removeObserver(this);
    super.dispose();
  }
}

Determining the orientation

Orientation is determined by the aspect ratio of the available size. This means that you can get the orientation in didChangeMetrics using the following code:

final orientation = WidgetsBinding.instance.window.physicalSize
    .aspectRatio > 1 ? Orientation.landscape : Orientation.portrait;

Example

I have constructed an example StatefulWidget that compares the OrientationBuilder callback to didChangeMetrics:

import 'package:flutter/material.dart';

void main() {
  runApp(OrientationListener());
}

class OrientationListener extends StatefulWidget {
  @override
  _OrientationListenerState createState() => _OrientationListenerState();
}

class _OrientationListenerState extends State<OrientationListener>
    with WidgetsBindingObserver {
  @override
  void initState() {
    super.initState();
    WidgetsBinding.instance.addObserver(this);
  }

  @override
  void dispose() {
    WidgetsBinding.instance.removeObserver(this);
    super.dispose();
  }

  @override
  void didChangeMetrics() {
    print('$WidgetsBindingObserver metrics changed ${DateTime.now()}: '
        '${WidgetsBinding.instance.window.physicalSize.aspectRatio > 1 ? Orientation.landscape : Orientation.portrait}');
  }

  @override
  Widget build(BuildContext context) {
    return MediaQuery(
      data: MediaQueryData.fromWindow(WidgetsBinding.instance.window),
      child: OrientationBuilder(
        builder: (context, orientation) {
          print('$OrientationBuilder rebuild ${DateTime.now()}: $orientation');

          return Container();
        },
      ),
    );
  }
}

Results

Running this example shows the following times for the two functions:

WidgetsBindingObserver metrics changed 2020-08-22 14:47:01.690172: Orientation.portrait
WidgetsBindingObserver metrics changed 2020-08-22 14:47:01.706574: Orientation.landscape
OrientationBuilder rebuild 2020-08-22 14:47:01.760589: Orientation.landscape
WidgetsBindingObserver metrics changed 2020-08-22 14:47:06.537083: Orientation.landscape
WidgetsBindingObserver metrics changed 2020-08-22 14:47:06.549545: Orientation.portrait
OrientationBuilder rebuild 2020-08-22 14:47:06.603859: Orientation.portrait
WidgetsBindingObserver metrics changed 2020-08-22 14:47:10.423787: Orientation.portrait
WidgetsBindingObserver metrics changed 2020-08-22 14:47:10.442866: Orientation.landscape
OrientationBuilder rebuild 2020-08-22 14:47:10.501729: Orientation.landscape
WidgetsBindingObserver metrics changed 2020-08-22 14:47:13.639545: Orientation.landscape
WidgetsBindingObserver metrics changed 2020-08-22 14:47:13.658906: Orientation.landscape
WidgetsBindingObserver metrics changed 2020-08-22 14:47:13.672025: Orientation.portrait
OrientationBuilder rebuild 2020-08-22 14:47:13.730771: Orientation.portrait

So in my case, the difference in detection was about 0.06 seconds.

Observations

As you can see from above, the difference is insignificant (I would say). So I am not even sure if this will be useful to you.

Moreover, I have observed that the OrientationBuilder callback is actually called at the start of the device rotation - at least on my Android emulator. This would mean that you can rebuild your UI before the rotation happens.

I hope this was somehow helpful to you :)

As you can see in this link, there is no "natural" way to do what you want:
https://github.com/flutter/flutter/issues/16322

Try to make something using this:

1. Lock the orientation: https://dev.to/mightytechno/how-to-change-screen-orientation-in-flutter-32c1
2. Listen to device rotation changes with this package (since the orientation will not change): https://pub.dev/packages/native_device_orientation
3. Make your customization
4. Set the new orientation using the link from step 1

You may try animated container for a better effect, but you would need to handle all the screen position and rotation manually before set the new orientation:
https://api.flutter.dev/flutter/widgets/AnimatedContainer-class.html

Something you might want to try is writing a platform channel method to get the sensor data from the accelerometer and then feed it to something like Transform.rotate().