RE: My QB Balance Sheet Report does not list the Beginning of Year and End of Year Inventory values under the GOGS header
GOGS is an expense and does not belong on your balance sheet.
Your inventory asset account will appear on your balance sheet.
To see the beginning and ending in inventory asset account balances for 2019, run the balance sheet for 12/31/2018 (which will show the beginning balance for 2019) and 12/31/2019 (the ending balance for 2019.)