No. You have to show that you were in the UK for exactly three years prior to the date that you apply. You cannot apply before you have been in the UK for at least 3 years. The application date is believed to be the day after you mail it, so if you send it on the first of the month, the application date is the 2nd. It can take a few months to process and it is advised not to travel during this time. After processing it can take a few weeks to have your citizenship ceremony.

You must also have a certificate of passing the Life in the UK test and have Indefinite Leave to Remain (ILR), so it may take five years to get you ILR depending on which path you are on.