How to create clean url for Default page in Yii2 urlManager

My index rules like as below:

[
    'pattern' => 'page/<page:\d+>',
    'route' => 'site/index',
],

it work, but in pagination, firest page is example/page/1, i change rules as below:

[
    'pattern' => 'page/<page:\d+>',
    'route' => 'site/index',
    'defaults' => ['page' => 1],
],

Now first page has become to example.com/page.

How write rules, to first page in pagination show like example.com?

As per your question in conjunction with your comments, I suggest that you additionally add a rule for a blank url pattern, i.e. for url with domain only, that is directed to your defaultRoute with a default $page parameter value.

'rules' => [
    [
        'pattern' => '',
        'route' => 'site/index',
        'defaults' => ['page' => 1],
    ],
    [
        'pattern' => 'page/<page:\d+>',
        'route' => 'site/index',
    ],
],

Then, in your controller action you can test this url rule is working as follows:

public function actionIndex($page)
{
    echo '<pre>';
    echo 'site / index / $page ' . print_r($page, true);
    echo '</pre>';
    exit;
}

Also note that you could set the default in the method declaration of your controller action like so:

public function actionIndex($page = 1)
{
    echo '<pre>';
    echo 'site / index / $page ' . print_r($page, true);
    echo '</pre>';
    exit;
}

Which would allow you to simplify your config as follows:

'rules' => [
    [
        'pattern' => '',
        'route' => 'site/index',
    ],
    [
        'pattern' => 'page/<page:\d+>',
        'route' => 'site/index',
    ],
],