I had that happen to me last year (but wasn't a major change as yours) when I was booked to fly from LAX - AKL in October.
I called Air NZ immediately when I got the notification in the app to discuss options.
Although there was an alternative flight available the same day I was asked to be put on the next available alternative flight which gave me an extra night in LA.
The original flight I was booked on - NZ5, was re-scheduled to the following morning. The alternative was NZ1 the same evening but timing wasn't suitable & PE looked chocker when I looked at availability.
So they put me on NZ5 the next day and I got the same seat assignment as my original flight.
In your case, contact centre staff may not have details regarding alternatives available just yet but I would still call and find out to discuss.