The optimization process and recommendations:

1. Avoid Calling Functions With Indexed Columns (query line: 20): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `day` is indexed, the index won’t be used as it’s wrapped with the function `DATEPART`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
2. Avoid Calling Functions With Indexed Columns (query line: 20): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `transactionTime` is indexed, the index won’t be used as it’s wrapped with the function `DATEPART`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
3. Avoid Subqueries (query line: 7): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
4. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.
5. Index Function Calls Using Generated Columns (modified query below): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index to optimize the search. Creating and indexing a generated column (supported in MySQL 5.7) will allow MySQL to optimize the search.

The optimized query:

SELECT
        a.year,
        b.month,
        c.day,
        totalVolume 
    FROM
        (SELECT
            DATEPART(year,
            DOW30.transactionTime) AS year,
            DATEPART(month,
            DOW30.transactionTime) AS month,
            DATEPART(day,
            DOW30.transactionTime) AS day,
            SUM(DOW30.volume) AS totalVolume 
        FROM
            DOW30 
        GROUP BY
            DOW30.datepart_year_transactiontime,
            DOW30.datepart_month_transactiontime,
            DATEPART(day,
            DOW30.transactionTime) 
        ORDER BY
            NULL) a 
    ORDER BY
        a.year,
        b.month,
        c.day