35 is a good age since you have enough experience in some sort of professional field. Assuming you can be a lawyer at 25 at the average rate of completing a Baechlor's degree and a law degree (typically a J.D) in 4 and 3 years respectively. That's 10 years of work experience in the legal field, and might suffice to be a head of state.
Even then, most people don't become heads of states at 35, it takes more years to enter the politics and become someone worth a shit.
"Bear Island knows no king but the King in the North, whose name is STARK."