Simply buying a cryptocurrency with fiat does not create a taxable event. You can refer to this list of taxable events to see what type of cryptocurrency transaction creates a taxable event.
Keep in mind, it is important to keep detailed records of when you purchased the cryptocurrency and the amount that you paid to acquire it. These records will establish a cost basis for these purchased coins, which will be integral for calculating your capital gains.
* For those reading who are unfamiliar, the term "fiat" typically refers to a country’s legal tender, such as USD or CAD.