flutter - correct way to create a box that starts at minHeight, grows to maxHeight

There's no notion of "Starts from max/min size".

The thing is, ContrainedBox only add constraints to it's child. But in the end, it doesn't pick a size.

If you want your child to hit minSize, then they have to not expend. Which translate into not having a width/height of double.INFINITY. Fact is that double.INFINITY is the default value of many widgets, including Container.

On the other hand, some widgets such as DecoratedBox have a default size of 0. Which means that this code :

return new ConstrainedBox(
  constraints: new BoxConstraints(
    minHeight: 5.0,
    minWidth: 5.0,
    maxHeight: 30.0,
    maxWidth: 30.0,
  ),
  child: new DecoratedBox(
    decoration: new BoxDecoration(color: Colors.red),
  ),
);

Will render a 5.0*5.0 red square.

Below Example will help you to grow Size of the widget as required

Container(
          color: Colors.blueAccent,
          constraints: BoxConstraints(
              minHeight: 100, minWidth: double.infinity, maxHeight: 400),
          child: ListView(
            shrinkWrap: true,
            children: <Widget>[
              ...List.generate(
                10,  // Replace this with 1, 2 to see min height works. 
                (index) => Text(
                  'Sample Test: ${index}',
                  style: TextStyle(fontSize: 60, color: Colors.black),
                ),
              ),
            ],
          ),
        ),

Output for Min Height for Single Item:

Output for Min Height for 10 Items:

Note: This will show widgets as per mentioned max-height.