If I signed a lease 3 days early from the date that the lease is to begin, can I change my mind about moving in?

I think that what you are referring to here is what is known as a "3-day right of rescission". Unfortunately, there is no right of recession with rental agreements. A lease is a contract, and as the saying goes, "A contract is a contract". In other words, once you sign the agreement, you are obligated for the full term of the lease. This is true whether or not you have already moved in or paid your rent/fees, etc. Unless of course the lease specifically give yo the right to terminate within 3 days.

However, a landlord is under a "duty to mitigate damages". What this means is that they must make a good faith and reasonable effort to re-rent the apartment and can only hold you liable for the period up to when they can re-rent it.

Also, since this all just occurred, speak to the landlord. They may simply let you out of your lease or will at least negotiate an early termination fee. If not, then you some options. You can try to find another person who can take you place and will enter into a new lease with your landlord or you can find someone who will sublet from you (you'll still be still on the lease and ultimately responsible for the rent but you'll at least have someone to pay the rent, or a part of the rent).