An advanced domain-specific search via Google may be more effective in searching for transcripts of the Ontario Legislative Assembly via Hansard.
It seems that a site-specific Google search tends to retrieve more results than the Advanced Hansard Search.
Navigate to Google.ca, at bottom right select "Settings" at bottom right of the page, then select "Advanced Search" (as shown below).
You can then search for your terms in the appropriate configuration in this site/domain: hansardindex.ontla.on.ca
Because it appears that not all transcripts include the date of the speech, if you need to be thorough or to limit the search to speeches/debates/statements made within a specific time frame, the advanced search is most accurate when you include a choice of any one of the the numbers that correspond to the particular sessions of parliament that you are interested in.
See the bottom half of this page for a listing of parliamentary session numbers along with their corresponding dates.
Below is an example to search for any mentions of a "poverty reduction strategy" from 2011-2021.
That time period includes sessions 39.2 up to 42.2 and all sessions in between (note that some parliament "cycles" have more sessions than others)