Magento 2: filter results by date, ->addAttributeToFilter

I am using the object manager (directly and intentionally) to get the sales quantity of a product.

$objectManager = MagentoFrameworkAppObjectManager::getInstance();
$product_id = 101;
$soldproduct = $objectManager->get('MagentoReportsModelResourceModelProductSoldCollection')
                             ->addOrderedQty()
                             ->addAttributeToFilter('product_id', $product_id)
                             ->getFirstItem();

This successfully allows me to get the quantity sold of a product by passing in the product ID to the attribute filter. Now I want to filter the results by a starting and end date…

$start_date = '2001-12-12 12:12';
$end_date = '2019-12-12 12:12';

… by adding this to the object manager parameters:

->addAttributeToFilter('created_at', array('from' => $start_date,'to' => $end_date))

But I can’t seem to get this code to work. How do I filter results by a starting and end date?