I saw the recent reader's question – "Why have Timothy circumcised after the council at Jerusalem?" And your answer "In regards to why Timothy was circumcised after the Jerusalem council, it is simply because Paul met Timothy after that council. Timothy wanted to join Paul, but because they were working among the Jews, Paul decided to have Timothy circumcised so that Timothy would be accepted by the Jews."
My question: How would anyone know? By the way, I truly enjoy reading and studying from your "encyclopedia" of Bible knowledge.
"Paul wanted to have him go on with him. And he took him and circumcised him because of the Jews who were in that region, for they all knew that his father was Greek" (Acts 16:3).
The Jews in the region would have correctly assumed that Timothy was uncircumcised and not a practicing Jew because of his father. It isn't that he could not enter the covenant. There are many examples of Israelites being circumcised later in life. For example,
"For the children of Israel walked forty years in the wilderness, till all the people who were men of war, who came out of Egypt, were consumed, because they did not obey the voice of the LORD-to whom the LORD swore that He would not show them the land which the LORD had sworn to their fathers that He would give us, "a land flowing with milk and honey." Then Joshua circumcised their sons whom He raised up in their place; for they were uncircumcised, because they had not been circumcised on the way" (Joshua 5:6-7).
There would be no need to lie about whether he was or not circumcised. A Jew who was concerned need only ask. It would be very similar to our asking a person if they were baptized (Acts 19:3). Of course, as Christians, neither Paul nor Timothy would want to lie, so the simple solution was to have Timothy circumcised as was his right under the Law of Moses. While Timothy would remain a Christian, he could be accepted in Jewish society.
But you should also keep in mind that it would be incorrect to apply our societal standards to the past. Common tasks such as bathing and other toiletries were not always done in complete privacy at all times. Even if a person were to lie about his status as an Israelite, it would eventually be exposed by either his lack of knowledge of the Law of Moses, the Hebrew language, or someone eventually noticing he was not circumcised.