You are receiving many different answers to your post because of the different assumptions that the readers are taking. For example, is the pipe system empty or filled? Is the startup against pressure or against no pressure?
If a centrifugal pump is started with the discharge valve fully open (versus throttled), the possibility of pump runout will increase; and the possibility of pump cavitation will increase. This may cause damage the pump. It is generally not recommended to startup into a fully open discharge pipe scenario.
At the moment when a pump starts, there is little frictional resistance to flow. Friction builds as the piping system fills. The pump operates at a very high flow rate during the period that the system is filling. The pump, at the moment of start-up, would have almost zero resistance and would operate at its right-hand most point of nearly max flow and zero TDH. Manufacturers refer to this as the run-out point. As the system fills, resistance would build until the design system curve is established. This is a characteristic of all centrifugal pump start-ups. Centrifugal pumps that have power curves that increase with flow should be started with a throttled discharge to prevent a high current condition associated with the combination of starting inrush current and maximum pump load. The notable exception to this are axial flow pumps which have a power characteristic that decreases with an increase with flow. For this reason, axial pumps should be started in a valve open condition.
The time it takes for the pump to accelerate (speed up) depends on the polar moment of inertia for the rotating parts and the accelerating torque. The accelerating torque is defined as the difference between available motor torque and load torque. The time it takes to reach nominal speed is depending on the size of the motor, but normal acceleration times are 0.1 s for small motors and up to 1 s or more for larger ones. The time it takes until the system has reached the final duty point is considerably longer. This time can be from a couple of seconds up
to a minute or longer for very large systems.
To answer your query, the pump operation may move from left to right or right to left on the pump curve depending on the particular scenarios. On an initial startup on an empty system, the pump operation would go left to right and then back left. On startup against pressure, the pump operation would go left to right.
See the discussion on pages 7-9 of the link below:
The correct procedure to start a centrifugal pump: