you can't. You come with your 90 day Non-O visa, go to immigration for a residence certificate, go to a mobile provider and buy a Thai SIM registered against your passport, then you go to a bank and open an account and transfer in a minimum of 800k baht to use for your extension of stay. Unless you are lucky enough to hold a passport pertaining to one of the diminishing number of embassies that still issue income certificates
Unfortunately for you the Canadian embassy stopped providing income certificates earlier this year so for your extension of stay you need 800k baht in a Thai bank account. For subsequent extensions you can show that you have transferred a minimum of 65k baht per month from overseas each month for the 12 months prior to applying so you need to start the transfers immediately, however you can spend the 65k as soon as it shows up in your account
it will be viewed as a border bounce. If you have zero previous history in Thailand you should get back in ok, but why would you when an extension provides the time you need. Just get the extension
In my view there isn't a huge difference between a single entry tourist visa and a visa exempt entry. When immigration says get a visa next time the generally mean one appropriate for the purpose of your stay