Use the global constant DATETIME_DATETIME_STORAGE_FORMAT to format the date:

    // If the time is in a different timezone then adjust it to UTC before you save it
    $date->setTimezone(new \DateTimezone(DATETIME_STORAGE_TIMEZONE));

    $paragraph = Paragraph::create([
      ...
      'field_date' => [
        'value' => $date->format(DATETIME_DATETIME_STORAGE_FORMAT),
      ],
    ]);