Isn't it more like the sound is there after the car has been standing for a couple of hours or so? The cold weather makes it worse.
I am facing the same in 2012 City iVtec M/T. The sound is more similar to say the plastic lining/shields rubbing against one another but actually it comes from the shocks whenever there's compression of the dampers.
The sound is there every morning but disappears/dampens after say 15 minutes of driving/manoeuvring.
I suspect the shock absorbers need replacement. Lets wait for the experts @Xulfiqar @rustam54 @capsat @SER_GTR .
How much miles has your car run? Mine is ~155,000.
Another issue i face is a crr crr crr sound whenever the car is in 2nd gear or above and between 1.75 and 2.25 rpm range. No sound if i stretch every gear from the very beginning. But if i drive with a light foot i.e. shifting gears at max 2.5k rpm with slow acceleration the sound is there in every gear except the first.