How do I grab the current product SKU in code, as early as possible?
Have you tried using menu_get_object?  It provides access to objects loaded by the current router item.

Once you've got the node, the product reference field is just going to list the products and Drupal Commerce may exclude products from the add to cart form based on rules and other modules.  But you can get the SKU of the first referenced product on the product display like this: 

$node = menu_get_object(); // May want to check that it's a node.
$node = entity_metadata_wrapper('node', $node);
$products = $node-&gt;field_product-&gt;get(0)-&gt;sku-&gt;value(); // field_product is my product reference, may want to check that it exists.