Lawrence Yates Sherman and J. Hamilton Lewis both became Senators from Illinois on March 26, 1913, with Lewis becoming senior senator due to the fact that Lewis is higher in the alphabet than Sherman (L is higher than S). So Lewis became senior senator immediately upon taking office.
Well, the same goes for Bartlett and Gruening, both of whom became first pair of Senators from newly-admitted Alaska (Bartlett ranking higher as former Delegate), as well as Oren Long and Hiram Fong, when Hawaii became a state (Fong ranking higher as former territotial Governor).
It's always a case with newly admitted states.