I thought there was some Flaw somewhere that provided a character with (extra) decrepitude, possibly from old wounds, but I may be misremembering it from previous editions... any help?
Otherwise, is it true that the the only way to start out a character with decrepitude is to ensure he starts at age 35+, and just roll for aging?
4th edition -2 flaw. In 5th edition, you have to be old enough to age (this doesn't need to be 35 if you have the Major Flaw that means you age more quickly, but I imagine you'd invoke that as a curse that started at a convenient age rather than at birth.)
As @darkwing says. Wounds do not result in decrepitude in 5ed AFAIR, so old wounds would not explain it. However, you have the malediction flaws which could surely cover decrepitude from more supernatural sources, if the troupe so wishes.
There aren't any flaws or other explicit mechanisms to add Decrepitude to a starting character - other than aging rolls.
But if you want a starting character to have some decrepitude then just add it to the character. Or make up a new Flaw for them to take if that would feel better.
It could also be a consequence of an established flaw like Lesser Malediction (or Greater, depending on the starting score).
Anyway I'd start thinking if the existing flaws aren't enough. A character starting with decrepitude seems odd to me because it refers very specifically to the mechanical procedure of aging. But what would it mean thematically? That he is fragile? Then what about picking Arthritis or Enfeebled?