travel to India with OCI or visa

Under ordinary circumstances, any traveler under 20 years of age needs to get the OCI card re-issued every time the passport is renewed. Source (emphasis mine)

(a) OCI card is a smart card;

(b) Possession of an OCI card will facilitate quicker immigration clearance at the Immigration Check Posts;

(c) It will help in obtaining various Consular Services from the Indian Missions;

(d) For those who are resident in India, it will facilitate in availing various services in India.

OCI card holders are required to get their OCI cards reissued whenever passport is renewed for persons under twenty years of age, and OCI card needs to be renewed after crossing 50 years of age only once, that too when the US passport is renewed.

However, in Dec 2019 Indian government had granted a temporary relaxation in rules (source from @phoog in comments)

December 18, 2019

?The following OCI guidelines have been in force since 2005:

OCI card needs to be re-issued each time a new passport is acquired by the cardholder up to the age of 20 years.

OCI card is required to be re-issued once on acquiring a new passport after completing 50 years of age.

Re-issuance of OCI card is not required each time a passport is issued to a cardholder between 21 and 50 years of age.

?This is to inform that Government of India has decided to grant temporary relaxation till 30th June 2020 in the following cases:

(i) In case an OCI card holder below the age of 20 years has not got OCI card re-issued on change of passport, he/she may travel on the strength of his/her existing OCI card bearing old passport number subject to the condition that along with the new passport, the OCI cardholder carries old passport mentioned in the OCI card.

(ii) In case an OCI card holder who has attained the age of 50 years and got his/her passport renewed subsequently but has not got his/her OCI card re-issued on renewal of passport, he/she may travel till June 30, 2020 on the strength of existing OCI card along-with the new and old passports.

It is, however, advised that OCI cardholders may take steps to comply with the existing OCI guidelines in Para 1 above and renew their OCI cards as required by the rules.

Recently (26-Mar-21), the relaxation has further been extended till 31-Dec-2021. Moreover they have also relaxed the need to carry old passport. Source

In order to further ease the travel of OCI card holders to India following has been decided:

(i) The time line for re-issuance of OCI cards in respect of OCI card holders, who may be required to get their OCI card re-issued, has been extended till 31 December, 2021.

(ii) Henceforth, the OCI card holders traveling on the strength of their existing OCI card bearing old passport number are not required to carry their old passport. However, carrying of new passport is mandatory along with the OCI card.

San Francisco March 26, 2021

In view of this your kid can travel on strength of his OCI card and new passport but it may be advisable to bring his old passport along, just in case.