If the Child is born in India and we have the GC by that time, is there any way the child can travel to US?

Your child may accompany you or travel with you to the U.S if the following conditions are met: 

a) the child has a separate passport; 

b) has a birth certificate from the corporation, municipality or a registrar of births and deaths (please note hospital records are not adequate) 

c) the child accompanies the immigrant mother or father upon her or his return to the U.S following the birth of the child 
d) the child is under the age of two years 

e) the immigrant mother or father has a valid Form I-551 or I-151, alien registration receipt card (in short called green card), or Form I-327 (permit to re-enter the U.S.) valid for two years from the date of issue.
 
If the above are satisfied then the child may accompany you into U.S without a visa. 

Following admission to U.S contact the nearest CIS office to regularize the stay of the child in U.S.