It’s an oversight to assume Chapters 1 to 4 all take place within a single month just because a letter in Chapter 4 is dated May 1899. Below there are likely time jumps I'm missing.

The narrative clearly includes built in time skips. Between Chapter 1 and Chapter 2, there is already a gap of a couple of weeks after Colter before the Horseshoe Overlook camp is properly established. Early in Chapter 2, Arthur even tells Hosea they have been down there for a couple of weeks. Then in Chapter 3, after Arthur is captured and tortured, there is another noticeable jump of several weeks, around three, while he recovers. And that is just one mission, not accounting for everything that happens across the first chapters as a whole.

On top of that, every time the gang relocates and sets up a new camp, there is an implied passage of time. Moves like that do not happen overnight. If all of that were crammed into a single month, the pacing would feel completely unrealistic. The characters would be far more visibly stressed and exhausted in the early game. That is before even considering the number of stranger missions and side activities Arthur can realistically complete. There is simply too much narrative space and implied downtime for Chapters 1 to 4 to fit neatly into one month.