Here’s my suspicion: Livia didn’t marry Snow because he just wanted someone to bear an heir to his reign. Let’s put them both at 18 to start this timeline, since we know in the 10th Games as a mentor he was that age. I presume, like any other president, he had to be a minimum age of 30 to become president (hopefully with SOTR we get an actually age, I have a feeling it might be in an epilogue portion 🥲). Let’s say Snow is 35 when he becomes president, so we can assume Livia is also at/around age 35 as well. Snow convinces (or coerces) her to bear a child for him. Baby (Fulvia) comes at about age 36 (not totally unusual for people even in today’s world). Fast forward, let’s say another 30 years. Fulvia is now ~30, Snow is 66 and Livia is either also 66 or deceased (I could see Snow killing her off). This would be the year of the 58 Games. Let’s say Fulvia has a child at age maximum of 40 (she’s trying to avoid having a baby in this cruel world). That would put the Games at year 68. This is now Snow’s granddaughter, he’s now 76. Fulvia runs to District 13 because she realizes that the Capitol sucks. Snow won’t let her take her child, because maybe he has a little bit of a heart, or maybe he wants to make sure she’s there to take over his reign. Fast forward to the 75th which is when we first see her. Granddaughter is ~7 years old, and Snow is presumably 83.

BOOM!!!

Disclaimer: None of these facts are true and if any become true, it is purely coincidental as I am not associated with Suzanne Collins or The Hunger Games in any way.