startActivity(FlutterActivity
        .withNewEngine()
        .initialRoute("/my_route")
        .build(currentActivity));

package com.peter.myapplication;
import androidx.annotation.NonNull;
import io.flutter.embedding.android.FlutterActivity;
import io.flutter.embedding.engine.FlutterEngine;
import io.flutter.plugin.common.MethodChannel;

public class BridgeActivity extends FlutterActivity {
    private static final String CHANNEL_NAME = "flutter.bridge.call_platform";

    @Override
    public void configureFlutterEngine(@NonNull FlutterEngine flutterEngine) {
        super.configureFlutterEngine(flutterEngine);
        getFlutterEngine();
        //config a method channel
        new MethodChannel(flutterEngine.getDartExecutor().getBinaryMessenger(), CHANNEL_NAME)
                .setMethodCallHandler((call, result) -> {
                    switch (call.method) {
                        case "testMethod":
                            result.success("This is respond result from Android native method");
                            break;
                        default:
                            result.notImplemented();
                            break;
                    }
                });
    }
}

public class MainActivity extends AppCompatActivity {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        // click button to jump flutter activity
        findViewById(R.id.tv_test).setOnClickListener((view) -> {
            Intent intent = BridgeActivity.withNewEngine()
                    .build(MainActivity.this);
            intent.setClass(MainActivity.this, BridgeActivity.class);
            startActivity(intent);
        });
    }
}

Intent intent = BridgeActivity.withNewEngine().build(MainActivity.this);
startActivity(intent);

public static NewEngineIntentBuilder withNewEngine() {
    //初步发现问题：这里直接写死了`FlutterActivity.class`，而非动态获取到`BridgeActivity.class`
    return new NewEngineIntentBuilder(FlutterActivity.class);
}
public static class NewEngineIntentBuilder {
    private final Class<? extends FlutterActivity> activityClass;
    private String initialRoute = DEFAULT_INITIAL_ROUTE;
    private String backgroundMode = DEFAULT_BACKGROUND_MODE;

    /**
     * Constructor that allows this {@code NewEngineIntentBuilder} to be used by subclasses of
     * {@code FlutterActivity}.
     *
     * <p>Subclasses of {@code FlutterActivity} should provide their own static version of {@link
     * #withNewEngine()}, which returns an instance of {@code NewEngineIntentBuilder} constructed
     * with a {@code Class} reference to the {@code FlutterActivity} subclass, e.g.:
     *
     * <p>{@code return new NewEngineIntentBuilder(MyFlutterActivity.class); }
     */
    protected NewEngineIntentBuilder(@NonNull Class<? extends FlutterActivity> activityClass) {
      this.activityClass = activityClass;
    }

    /**
     * Creates and returns an {@link Intent} that will launch a {@code FlutterActivity} with the
     * desired configuration.
     */
    @NonNull
    public Intent build(@NonNull Context context) {
      //build方法里，直接使用NewEngineIntentBuilder Constructor传入的activityClass构建Intent
      return new Intent(context, activityClass)
          .putExtra(EXTRA_INITIAL_ROUTE, initialRoute)
          .putExtra(EXTRA_BACKGROUND_MODE, backgroundMode)
          .putExtra(EXTRA_DESTROY_ENGINE_WITH_ACTIVITY, true);
    }
  }

Intent intent = BridgeActivity.withNewEngine().build(context);
//重新设置一下目标class到子类BridgeActivity.class
intent.setClass(context, BridgeActivity.class);
context.startActivity(intent);

public class BridgeActivity extends FlutterActivity {
    //...
    //继承`NewEngineIntentBuilder`调用被`protected`修饰的Constructor
		public static class MyNewEngineIntentBuilder extends NewEngineIntentBuilder {
        MyNewEngineIntentBuilder(@NonNull Class<? extends FlutterActivity> activityClass) {
            super(activityClass);
        }
    }
    //接着则可以按提示自行提供withNewEngine()返回用子类构建的`NewEngineIntentBuilder`
    public static FlutterActivity.NewEngineIntentBuilder withNewEngine() {
        return new MyNewEngineIntentBuilder(BridgeActivity.class);
    }
  
    //类似的，如果有使用CachedEngine，也可能继承`CachedEngineIntentBuilder`调用被`protected`修饰的Constructor来返回用子类构建的`CachedEngineIntentBuilder`
    public static FlutterActivity.CachedEngineIntentBuilder withCachedEngine(@NonNull String cachedEngineId) {
        return new MyCachedEngineIntentBuilder(BridgeActivity.class, cachedEngineId);
    }
    public static class MyCachedEngineIntentBuilder extends CachedEngineIntentBuilder{
        protected MyCachedEngineIntentBuilder(@NonNull Class<? extends FlutterActivity> activityClass, @NonNull String engineId) {
            super(activityClass, engineId);
        }
    }
}

//直接跳转，不使用cacheEngine
Intent intent = BridgeActivity
            .withNewEngine()
            .initialRoute("initialRoute")
            .backgroundMode(FlutterActivityLaunchConfigs.BackgroundMode.transparent)
            .build(context);
context.startActivity(intent);

//使用cacheEngine跳转
Intent intent = BridgeActivity
        .withCachedEngine("your_cache_id")
        .backgroundMode(FlutterActivityLaunchConfigs.BackgroundMode.transparent)
        .build(context);
context.startActivity(intent);