Grandfather paradox is meaningless since time has a rate of flow?
Time has a rate of flow. Assume the rate of flow of time in 2019 suddenly decreased compared to 1963. This will enable changes in 1963 to reach 2019 but it might take thousands of years in real time for this change to creep to 2019 depending on the difference in time rate of flow.
The most rational assumption is that there is only one timeline. This timeline has an ambient rate of flow of time. This rate of flow of time can be changed yet it is mostly a constant.
A person who will travel backwards in time will need first to change the rate of flow of time inside a vessel to be negative compared with the ambient rate of flow of time. Inside the vessel there will be another vessel which will have a rate of flow of time negative to the initial one thus negating the effect of flow of time on the person while keeping it working compared to the ambient rate of flow of time outside. This will enable a time traveller to travel to the past instantly.
While a time traveller can travel instantly his vessel will actually experience the whole difference in time.
Once the time traveller reach 1963 and change something this change should never alter the future if the ambient rate of flow of time is constant. If there is a slight difference this change will creep to the future.