How to find MIN() of sorted aggregates without using loops

I have a table that my daily script sends the findings to. It looks something like this:

I want to find out the date when the current set of issues started for every product (i.e., the latest date when issues_found turned from 0 to non-zero), and add it to another column. So the table should become something like:

My approach is to iterate over date-sorted records for every product and break when 0 is encountered:

DECLARE found_date DATE;
FOR row in (SELECT * FROM my_table)
DO
  SET found_date = NULL;
  FOR historical_entry in (SELECT * FROM my_table WHERE product = row.product ORDER BY run_date DESC)
  DO
    IF historical_entry.issues_found <> 0 THEN
      SET found_date = historical_entry.run_date;
    ELSE
      BREAK;
    END IF;
  END FOR;
  UPDATE my_table SET issues_started = found_date where product = row.product;
END FOR;

It's a very procedural approach and although it works, it takes hours when run against hundreds of products and thousands of records. Is there a better approach than two nested loops? I tried using MIN(run_date) over aggregates of non-zero issues_found rows but couldn't quite get it right.

Consider below approach

WITH issue_starts AS (
    SELECT
        product,
        run_date,
        issues_found,
        CASE
            WHEN issues_found <> 0 AND IFNULL(LAG(issues_found) OVER (PARTITION BY product ORDER BY run_date), 0) = 0 
            THEN run_date
        END AS start_of_issues
    FROM your_table
), latest_issue_start AS (
    SELECT
        product,
        run_date,
        issues_found,
        MAX(start_of_issues) OVER (PARTITION BY product ORDER BY run_date ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) AS issues_started
    FROM issue_starts
)
SELECT
    t.product,
    t.issues_found,
    t.run_date,
    l.issues_started
FROM your_table t
JOIN latest_issue_start l
ON t.product = l.product AND t.run_date = l.run_date
ORDER BY t.product, t.run_date DESC

if applied to sample data in your question - output is