Step up converter 1-3V to 5V fixed for supercapacitor
First page of the datasheet, left hand side says "Operates at Supply Voltages from 1V to 30V".

Page two says "input voltage... step up mode... 1.0 (min) 12,6 (max)".

Page 6 says input  of 1.05V, output of 5.

So, the datasheet says in three places that it will work.