They do not know how long they have pondered this question. Has it been 10 months, or 10 millenia? Eggo can not even track time with dates. In fact, it would be impossible to.
To understand this, it is imperative to understand Eggo's ability: Egg Magic. No true explanation of the power exists, and no laws of physics ever seem to contain it. The flow of time and the space between space all seem to bend to their will, making a mockery of modern science even in EF cities final days. The only true known limitation of the power is it's inability to control the minds of others as Eggo themself has stated.
And so Eggo became a drifter in time and space, searching for their past to only find their future. As the weary traveller became dulled to the bending of time, there were two paths ahead of them. The first - nihilism - realising the world's before them had no meaning. That they could see everything live and die before them, knowing there was nothing more they could have done. The second, that while time showed every big moment, it could not capture the majesty of everything small. It was on arrival in EF city that Eggo chose their path. The second path.
You can keep some notes on this character. You'll be the only one to be able to see this: