Mohan,
Welcome to the forum community.
Like any garden plant, fig plant growth can be timed backwards. It also depends on several factors including vigor of the cultivar and ambient temperatures.
30 - 45 days for rooting @ 70*F - 75*F.
30 - 60 days for root development @ 70*F - 75*F
30 - 60 days to develop branch growth @ 70*F - 75*F
~ 90 - 165 days before setting out.
During this time the cutting may have been transplanted to progressively larger containers as much as 3 times, depending on the rooting and growing method. Like Kelby, I place all my plants in South and East facing windows and have had good healthy growth. If you have the space and light fig cuttings can be started year round indoors.
Good Luck.