Qur'an

10:5. It is He Who made the sun to be a shining glory and the moon to be a light (of beauty), and measured out stages for her; that ye might know the number of years and the count (of time). Nowise did Allah create this but in truth and righteousness. (Thus) doth He explain His Signs in detail, for those who understand.


In my humble opinion this is conclusive proof, that the best way to determine a date is like we do in our everyday lives, we use a clock and calendar and the cycle of the moon (whether we can see it or not, if we know it is there by calculation there is no need to see it).

It happened so at the time of the Prophet (Peace and Blessings Be Upon Him) that man didn't have the knowledge to make the calculations of time and cycles of the moon that modern science and math have afforded us today, but clearly this verse takes precedence over any verse that implies the moon must be sighted.