No one will ask you to "prove" it. When uploading your passport pages, IRCC expects you to upload your current valid passport only, even if it's a brand new unused one.
You are required to list your travel history, that's it. Some countries don't even stamp your passport, for example if you travel within the Schengen countries. You would still need to list all travel in the past 10 years, because they will find out during the background check.
If you can't remember the exact dates, make your best guess (you can try looking through your email inbox for old tickets, or check dates on your social media if you uploaded travel photos). You can also mention that you don't remember exact dates in an LoE.