Here's an interesting question (at least I find it interesting!): In an unfallen world, would God intervene more often or less often?
On the one hand, it might seem that God would intervene less frequently–if at all. It's often said that sin creates a barrier between God and man. Sin separates us from God. Sin disrupts our fellowship with God. Sinners can't approach a holy God directly. We need buffers (the Mosaic cultus) or a mediator (Jesus). On this view, God keeps his distance in a fallen world. God "hides" himself–a recurring theme in the Psalms.
An unfallen world might still be a hazardous world. There might be major predators outside Eden. There might be natural disasters (e.g. floods, hurricanes, tornadoes, earthquakes, wildfires, meteors), but God would providentially or miraculously protect us from natural evils. In principle, God could protect us without our awareness of divine protection.
In theory, an unfallen world might resemble a "godless" world in the sense that there might be no occasion for God to manifest himself more overtly (e.g. theophanies, angelophanies, dreams, miracles, answered prayer, an audible voice). God would remain in the background, protecting and providing for us behind-the-scenes. An unfallen world might operate like a clockwork universe. In a world like that, there's not much to pray for.
On the other hand, redeeming a fallen world requires conspicuous divine intervention. A fallen world is a theater for divine intervention. In a way, that's why it exists. It's designed to cultivate a sense of utter dependence on God. God intervenes in a variety of ways that are often conspicuously "unnatural". In striking events or communications (e.g. theophanies, angelophanies, dreams, miracles, answered prayer, an audible voice) culminating in the Incarnation and Resurrection–with the Parousia to come. It may be that in a fallen world, God necessarily takes a more hands-on approach.
Jews and Christians often have a sense of divine absence or abandonment. Much of the time, maybe most of the time, it feels like a "godless" world, as if things just happen automatically. Everything happens just like clockwork. Trapped in the cycles of nature. Forced to live as if atheism is true.
Yet, ironically, it's arguable that however intermittent, a fallen world is characterized by conspicuous divine intervention–whereas God's existence would be far more oblique in an unfallen world.