"in the first days" is correct and usable in written English. You can use it to refer to a period of time at the start of something. For example, "In the first days of the new semester, the students all felt excited about the year ahead."
All revolutions are blissful in the first days.
Gilson lost his house in the first days.
Things looked grim in the first days of his trial.
In the first days, the choice was clear.
In the first days after birth it can be dangerous.
Nights of clumsy lovemaking in the first days of marriage.
Or in the first days of the anti-Assad demonstrations in Damascus.
to explore Italian mothers' perception of latching difficulty in the first days postpartum.
Changes were more evident in the first days after manufacture leading to stabilization over time.
In the first days of the crisis, coroner Robert Treuting saw five suicides in three days.
Demand for the phone was remarkably strong in the first days.
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia