If I signed a lease but changed my mind within 24 hours, and never took possession, can i get out of the lease?

You don't have many legal options. Having signed a lease, you may be held to its terms--including paying rent for the term of the lease. The fact that you never took possession does not matter. The landlord has a duty to reduce (mitigage) his/her damages by re-renting the apartment and may not hold you liable under the lease once a new tenant starts renting. However, while the landlord must make a good faith effort to re-rent, that's no guarantee of success. You can help them and yourself by finding someone who will take over from you, either as a sublet or an assignment. However, legally, you are responsible for the rent for the lease term or  until the space is rented to someone else.