You can't forget the tracks already exist in most of these places. We had a rail network until the car became our main mode of transport. It is a long timeline that can be accelerated, as others have said.
The regional airport/Banff train is an obvious first step, then commuter trains, and then you can look at more tourist/economically feasible destinations. I actually don't think HSR is the answer to most of these and instead fairly inexpensive rolling stock and some pullout track is all that's really required.
I'm obviously over simplifying it but there are quick easy wins available here. Your highest frequency would need to be airport to downtown via a nose creek transfer. Other wise you can run at commuter times in the morning and afternoon from the currently tracked suburbs and between the airport and Blue Line extension stop for people who work at the airport (or run it all day?). You can do three trains daily between Calgary and Banff that can feed Cochrane and Canmore commuters. Eventually or maybe even right off the start, add Friday and Sunday night trains between Edmonton, Red Deer, Calgary, and Lethbridge and that is a realistic first step.
Airdrie>Calgary
(1 Train, hourly round trip)
6:30AM > 7AM (Stop at Nose Creek Airport Transfer Station 6:45 (return trip 7:15))
7:30AM > 8AM (Stop at Nose Creek Airport Transfer Station 7:45 (return trip 8:15))
8:30AM > 9AM (Stop at Nose Creek Airport Transfer Station 8:45 (return trip 9:15))
4:30PM < 4PM (Stop at Nose Creek Airport Transfer Station 4:15 (return trip 4:45))
5:30PM < 5PM (Stop at Nose Creek Airport Transfer Station 5:15 (return trip 5:45))
6:30PM < 6PM (Stop at Nose Creek Airport Transfer Station 6:15 (return trip 6:45))
Okotoks>Calgary
(1 Train, hourly round trip)
6:15AM > 6:45AM (Stop at Chinook C-Train Transfer Station 6:35 (return trip 6:55))
7:15AM > 7:45AM (Stop at Chinook C-Train Transfer Station 7:35 (return trip 7:55))
8:15AM > 8:45AM (Stop at Chinook C-Train Transfer Station 8:35 (return trip 8:55))
4:45PM < 4:15PM (Stop at Chinook C-Train Transfer Station 4:25 (return trip 4:55))
5:45PM < 5:15PM (Stop at Chinook C-Train Transfer Station 5:25 (return trip 5:55))
6:45PM < 6:15PM (Stop at Chinook C-Train Transfer Station 6:25 (return trip 6:55))
Airport>Nose Creek Commuter Transfer Station
(1 Train, 15 minute round trip)
Airport>Blue Line
(1 Train, 15 minute round trip)
So, in this phase you need 6 rolling stock to have 4 trains working at once and 2 spare that can supplement the airport trains and allow for maintenance. New track is required between Nose Creek the airport and Blue Line but other wise the new track is minimal outside of some pullouts.