Please refer to wiki if you want to learn about how the historians and scholars date the birth of Jesus. It is quite long, and it is a good read to be done individually.
But as regards to the number of the beast (666) the bible give many hints. First, the bible teaches that beast have horns, heads and crowns. It also teaches in Daniel 8 that, a beast represents a kingdom, or several kingdoms, a horn symbolically represents a king or a kingdom of a beast that rules for many years. Thus, the number of the beast, would be the number of a man who is a king of this beast. Now, the scriptures gives many hints, which are compatible with the Ummayads:
1. The beast makes war with 2 witnesses - compatibility is seen when we notice in Quran Muhammad and Ali are called witness, and Ummayads were in war with Muhammad and Ali.
2. The beast has 7 heads, 10 horns - compatibility is seen when we notice Ummayads ruled over Seven dominions and their kings had 10 names.
3. The number of the beast is 666 - compatibility is when we see Muawwiah who was one of the kings of Ummayads, became Caliph in 661 AD (which would be 666 years after Christ). In this year, he killed Ali, one of the witnesses.
The above points, you have already seen. But there is another one, which it has not been discussed or noted before, and that is in Daniel 8:
When we read Daniel 8 from its beginning, we notice how compatible it is with history.
It starts from the time, the Kingdoms of Persia and Media were very strong, and then it describes how the Alexander the Great defeated Persian Kingdom, and later how there appeared 4 kingdoms after Alexander the Great.
Now, here comes the hint: Notice that according to history, the Emperor of Byzantine came to existence through appearance of the Kingdoms of Greeks, namely after the Alexander the Great, and the 4 kingdoms described in Daniel 8.
Now, according to history, which you must be familiar with to understand this, the Empire of Byzantine was replaced by Ummayads. This in chronological order is described in Daniel 8:
9 "Out of one of them came another horn, which started small but grew in power to the south and to the east and toward the Beautiful Land."
Notice how clearly, this prophecy is talking about Caliphate of Ummayads, who began to grow in the same region as Byzantine and then grew in power more and more. It even came to the Beautiful Land, which is the Holy Land of Israel. Now, this horn, which began to grow, appeared in 661AD, when Muawwiah established the Umayyad Caliphate. See how closely and clearly the history is compatible with the description of the Beast? Please try to make yourself more familiar with the history. It will help you see the compatibilities better. Then you will recognize when the meaning of the symbols understood correctly, there is a 100 % compatibility with history, and 0% mismatch.