how can buildings constructed fast under initial stage of construction possess strength to bear designed load when the concrete attains its maximum strength only after 28 days?
Because most buildings cannot be constructed fast enough for strength to be an issue. If it is clearly anticipated to be an issue, then the strength of the concrete can be designed to accommodate the speed of construction.
Often in high rise concrete buildings, shoring is removed in as little as 7 days after placing and re-shores are installed. Typically, they measure concrete strength for periods longer than 28 days because of the length of time it takes to construct high rise buildings. Concrete strength taken at 56 days or 90 days is quite common.