Here is the situation in brief:

Landlord and tenant signed lease, and agreed landlord's realtor would deliver keys to property upon receipt of payment of security deposit and 1st month's rent. (Landlord lives a couple hours drive away.)

Tenant lied to realtor claiming he had given a check to the landlord, and realtor turned over keys.

Tenant moved in, and after a week, has evaded all phone calls and has not paid rent.

Question: If there has been NO payment, is it possible to rescind or nullify the lease and thereby abbreviate the eviction process?

First if I was the landlord I would be holding the realitor liable for the money at this point, ( which is why they carry errors and omission coverage) because the realtor should not have turned over keys without knowing.

Next the tenant could maybe have criminal charges for fraud charged,since he lied about paying the money to fraud the realtor.

I would look at it as they committed a criminal act ( assuming you have that clause in the lease) or follow the non payment
Also the realtor should be sitting on the door set waiting on the money since they messed up.

But also why was the lease signed ( and them given a copy when there was no money given, money is given at the time of the papers signing)
But in general you need to start your eviction procedure

Sounds like you may have to go through the eviction process. Here is a link to a licensed attorney in Arizona who is specialized in real estate law. You should be able to get your question answered here.

www.askthetitleman.com