Based on the (Happiest) idea that free falling is an inertial frame, coupled with already known fact that different masses fall at same pace as reinforced by the Eötvös Experiments — Einstein intuitively concluded that massless objects (i.e. light) should also fall at same pace.
Step-2: So light also falls but it cannot get increasing speed because according to Einstein’s own principles light could not get increasing speed.
Step-3: Light can fall towards gravity but cannot accelerate by way of increasing speed. So what were other commonsense or intuitive options? There were two commonsense based philosophical answers. (1) Light could accelerate by way of change in direction (bending of light) and; (2) by way of blueshifting.
Step-3: Commonsense conclusion: Falling light is getting blue shifted. Its commonsense meaning is that frequency of light is increasing. Frequency of light itself is time clock. So time is getting speed up near the massive object.
Oh… What? Time speeds up near mass? But official physics says that time slows down due to mass. Well, following is the actual official position, fortunately well explained by Mr. Allen Everhart:
They (gravitational redshifting and time dilation) are the same thing. The time dilation near a massive body makes oscillations take longer when viewed from higher altitudes. If the oscillator is an electron then the frequency of light received at higher altitudes will be less than that which an observer at low altitude observes is emitted.
So leave aside whether time is slow or fast near mass … Official position is that time appears to slow down near mass when viewed from higher altitude. This position is confirmed by other experts also. For example, George Dishman writes:
The same effect applies to clocks, a clock on the surface of the Earth would seem to run slower as seen from orbit, and GPS clocks in orbit run faster than those on the ground.
However, his mention of “GPS clocks in orbit run faster” makes it confusing. This is not clear position and situation is still fishy. What is more appropriate is that official concept of gravitational time dilation is a relative concept i.e. not an absolute concept. Time near mass only seems to be slowed down as seen from orbit in higher altitude. But still the confusing aspect is about GPS clocks for which explanation by experts in invited in the comments section.