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Here's how I've opted to do it. Please do submit alternative answers if there's a better way.

Use the civicrm_post hook like this:

Note that you need to replace N with your custom field's ID number

function myext_civicrm_post($op, $objectName, $objectId, &$objectRef) {

  if ($objectId && $op == 'create' && $objectName == 'Contribution') {

    // See if we have a field that belongs to the fieldset.
    $result = civicrm_api3('CustomValue', 'get', [
      'sequential' => 1,
      'entity_id' => $objectId,
      'entity_type' => "Contribution",
      'return.custom_N' => 1,
    ]);

    if ($result['count'] == 0) {
      // Create the default entry.
      $result = civicrm_api3('CustomValue', 'create', [
        'sequential' => 1,
        'entity_id' => $contribution_id,
        'entity_type' => "Contribution",
        'custom_N' => 'unknown',
        // custom_M ...
      ]);
    }

  }
}

Then when you create a Contribution, the defaults are properly set.

Interesting observations

My interest was in creating the default record when the contribution was created by the API. But I thought I'd look into how this works with using the UI too.

If you use the web UI to create a contribution then the code above gets in before the main process creates/sets the custom values. i.e. This is the order of things:

1. User creates a contribution record.
2. Contribution record created.
3. Our hook runs, no custom value exists so it creates the default record.
4. The user-entered values (inc. the defaults that were set up in the form) overwrite the default created by our hook.

The same process happens when you use the API to create a contribution but include values for the custom data also.