Is it possible to learn to fly and become an airline pilot within
about 3 years (let's say age 20-23), then immediately get employed as
an airline pilot and fly intercontinental routes (even as a co-pilot)?
Yes, but not in the US. You'll have to look overseas at airlines like Emirates/Qatar etc. for that.
Airline routes are offered by seniority; and pilots that have been with the airline a significant amount of years (I am talking 5+ at minimum) are given the longer routes.
In the US, where I have the most exposure to the flight training side - once you get your ATP (Airline Transport Pilot) and have acquired all the relevant type certifications - your entire purpose in life is to build up your hours as PIC (Pilot In Command) / PF (Pilot Flying).
You will be doing this on regional airlines, which may be contracted out to larger airlines. You may be flying an aircraft that's painted in United colors, but its actually a regional airline used on "feeder" routes to the larger hub airports. This is typically the case in the US (and Europe).
Or, you may be employed by an airline that has no international routes.
Outside of these areas - if you come to the Middle East, you may be flying international routes at the start of your career; simply because that's the only option - and you may be flying the long haul jets if that's all the airline has to offer.
For example, Emirates (the largest operator of 777 and the A380) flies international exclusively; and the majority of their routes are medium to long haul (greater than 3 hours flight time). You may have a chance to fly internationally, but on shorter routes like Dubai - Muscat, Dubai - Bahrain, Dubai - Kuwait (this is the shortest A380 flight by Emirates, and is used for crew training/familiarization).
Qatar Airways is similar - they use their short routes for crew familiarization and training on their newer aircraft. They flew their 777-200/300LR on the Doha - Kuwait - Doha circuit when they first got the aircraft (a route normally served by the A320); and the 787 on the Doha - Dubai - Doha circuit (again, normally served by the A320).
However, you may not have the opportunity to fly the longer routes until well into your career with the airline; and you will be starting off (training) in smaller aircraft and a lot of simulator time.
Typical training period for commercial pilots is between 3 and 4 years (if you are directly trained by an airline, such as Emirate's flight training program) and then you are qualified as an airline pilot.