Ohh, let's not go there. I'm of the opinion that there is no such thing as fate in the Berserk universe because of the plays on duality.
Is everything controlled or does everyone have free will? It's an age old question but Berserk has its own special answer. The answer is both.
The Idea of Evil character is canon as it appears for one panel and Griffith and IoE had a talk, but the chapter is not, but it serves as a good explanation for what is going on. We don't truly know how causality is manipulated or how the God Hand influence the world, but they do. IoE gives us a small hint at how he does it. It says >I control the lesser subconscious emotion of people
Essentially, IoE is doing a very large keikaku on the entire world while having very very limiting control. And that's pretty insane. So yeah, everyone has free will and can decide for themselves but IoE, and possibly the God Hand, do a slight touch on people to affect them.
I also think that IoE and the God Hand only manipulate people, not magical beings or the physical world. Which makes the manipulation of causality even more insane. This is why Void talks endlessly about the flow of causality and its inevitability.
There was no certainty that Griffith would've accepted. Much like the Count earlier in the story, Griffith could have simply refused the offer. Skull Knight even talks, after saving Guts and Casca out of the Eclipse (I think?) that fate is not decided. In big moments, small actions can change the flow of causality. This is why Skull Knight tried to attack Griffith as he killed the Emperor, but it turned out that this small action was also within the flow of causality.
To bring more focus into this, after Skull Knight saves Guts and Casca, the God Hand lament that they couldn't see it coming and that they don't see everything. However, you'll notice that Rickert was outside, waiting, with a bag of fairy dust to heal Guts and Casca as if it was manipulated. This was done by IoE.