Creating backups on Alwayson without differential backups
. I don't plan to create any differential backups for the AAG group. Can you please let me know if enabling this option should work.


Yes, it'll work.


  Is it true that for new databases, only full backup happens and not the log backup?


I don't understand the question. If it's specific to Ola's script then I do not know, if it's a SQL Server question then you must take at least one full backup and one log backup before adding the database to the AG, so the answer would be no it isn't true.


  What can I do to resolve the issue?


I currently do not see an issue. It's a valid backup strategy, now where or not it meets your recovery SLA in a disaster is another question.