In Canada, if you buy a
Canada Post "Official First Day Cover", it is already cancelled and cannot be mailed, even on the first day of issue.
However, you can buy the stamp on the first day from any outlet, place it on an envelope and mail it to yourself. You will get a cancellation showing the first day of issue
date but it won't say "First Day Cancel" within the cancellation itself.
In the USA I believe that only one city is designated as the "first day city" and the stamps are only available at that one city on that date (at least it used to be like this; is it still like that today?). If you happen to be at the right location in that city you can buy the stamp(s) on the day of issue and get them cancelled. Collector-produced first day covers are
very popular in the United States (not so in Canada).