I got this error three or four times during my installation and finally got the solution how to bypass this error.
This error comes about because the account which the user selected on the Server Configuration page during installation is somehow not able to bring the SQL Server database engine services online. Instead of using build in account for the services, use Domain account.
In this service account, I used domain account instead of build in account
In Database Engine Configuration, Use mixed mode (SQL Server Authentication and Windows Authentication)
Above steps will solve the problem which you encounter “SQL Server install error Wait on the Database Engine Recovery Handle Failed”
Aryan Nava 