As far as I am aware you would have to keep hitting load more until you found it. Unfortunately the activity log is still pretty much in its infancy without any filtering or searching. There is the events API endpoint which will let you view the events (activity) for specific things like products.
So you may be able to query the events, The only problem is of course that you won't be able to query the product specific events since the product no longer exists, and the log for deleted products doesn't get kept, meaning you can't referece the logs via the product_id, though the log itself still exists.
So you are pretty much left with the base event.json endpoint with a filter=Product and perhaps add a timeframe, if you know when it happened.