You need to add some time for the rotation to gather enough angle of attack change so the aircraft can lift off. While the pilot pulls to lower the tail and rotates around the main gear, the aircraft continues to accelerate. Also, the 1.3 factor is only required to be reached once the aircraft climbs through 35 ft (or 50 ft, depending on the certification). What happens is that the pilot starts pulling right around stall speed, the aircraft starts to produce more downforce at the tail until the nose gear lifts off, then rotates until the angle of attack has grown to maybe 10° so the wings create enough lift for take-off. At this time, the aircraft will have accelerated to around 1.15 times stall speed and starts to climb, which requires still more pitch change. Now drag will increase by the amount of induced drag produced by the added lift so the rate of acceleration slows down. Still, until the 35 ft are reached the aircraft will accelerate further to 1.3 times stall speed at this point.
That is how the take-off distance is flown for certification to achieve the minimum distance. Depending on the rotation rate (typically 3° to 5° per second) and excess engine thrust, the optimum take-off might require to start the rotation process at less than stall speed. For added safety, it is advisable to stay a little longer on the ground if the available runway permits it.