It is always a good idea to get a copy of every document you sign-when you sign it. That is for YOUR protection! IF you don't have a copy, who is to say that all the info that is on the papaer was there when you signed it.
That being said, Not being in possession of a copy of the lease is not reason for the lease to be negated---who is to say that you DIDN'T get a copy, and possibly have mislaid it?
Contact your landlord (or their agent) and request a copy of the lease. Then look at the terms, and ask under what terms you can be released from your contract. There will certainly be some consequences to be paid, but it may be that a release is possible, with less repercussions then you fear.
A good agent will try to re-ent the unit as quickly as possible and should be able to release you once another renter is in place. If there is a high demand for that unit you may only have relatively small re-rental costs to cover.
Blessings to you as you pursue the right path to resoultion
I agree with the other answers in that possession is not an issue. You should have some type clause in the agreement that will tell you how to end the lease. I would request a signed copy from your landlord and I would be happy to take a look at it for you. Goodluck!