How can I find out what my inventory stock quantities were as of a specific date?

Using the Inventory Movement Summary Report will allow you to filter for a specific date range.

Filtering for a date range will summarize the totals so if you look at the Sum Qty Column it will display the summarized total for the quantities for all of the transactions that happened in the date range filtered.

It is re commended that the date range start date be a date before you even started using the company file, like 01/01/1970.