New Tickets visible for all groups in an Entity

Suppose to have an entity with three groups (Client, Support I Level and Support II Level).
I would like to have the following behaviour:
- when an user from Client group creates a ticket, this is automatically assigned to Support I Level group without being visible to the Support II Level.

The problem is when a ticket is in status "NEW" and all the groups have the property  "Assign" enabled, the ticket is visible by all of them.

This behaviour is a huge problem according to ITIL v4 Foudation best practices form Information Technology Service Management.

It could be possible to implement a solution for this problem?

Regards,
Andrea