When Henry Clay first became a United States Senator in 1806, he was not yet old enough to meet the constitutional requirements of the office.
Henry Clay first entered the Senate when he was some months under the constitutional age of thirty years, having been appointed by the governor of Kentucky to fill a vacancy in that body. The reason why this was allowed and was not made a subject of protest is found in the fact that Clay was universally believed to be more than thirty. He had had an elder brother, also named Henry Clay, who died while quite young. The record of his birth was supposed to be the record of the birth of the great Henry Clay, who was therefore thought to be constitutionally eligible in respect to age. When the facts finally came out, Clay was past thirty, and so there was nothing to do about it. The case, however, is unique in the annals of American history. [Link]Well, not exactly unique. Armistead Thomson Mason of Virginia was a few months younger than Clay when he was sworn in in 1816, and John Henry Eaton of Tennessee took his oath of office in 1818 at the tender age of 28.
Apparently no one asked John Eaton how old he was. In those days of large families and poorly kept birth records, he may not have been able to answer that question. Perhaps it was only later that he determined the birth date which now appears on his tombstone, confirming his less-than-constitutional age. [Link]Two other Senators were elected at age 29, but waited until after their birthdays to be sworn in: Rush Dew Holt of West Virginia in 1935, and Joseph Biden of Delaware in 1973.