"In a first step" versus "In the first step"

Question

In German we would often use the phrase "In einem ersten Schritt" which literally translates to "In a first step[, we did this or that..]". It is often used when the order of steps is a bit arbitrary.

This is in contrast to "Im ersten Schritt" ("In the first step") which is often used when the order of steps is more obvious or natural.

Now Google Doc always suggests that I should change "In a first step" to "In the first step" and I wonder how native English speakers fell about this. Does "In a first step" feel right to you under the conditions mentioned above?

Example: In a first step, the police officers examined the alibis of possible suspects. In a second step they searched for witnesses in the neighborhood. (here, the second step does not necessarily depend on the first step and there would be multiple possible first steps)

Here's a similar, but not identical question:

Why "a" before "elements of a first step"?

Answer 1

It doesn’t feel like there is any idiomatic force behind either alternative — that is, it’s not a common expression in English. We are much more likely to use other forms like “First of all…”, “Initially…”, “Firstly…”. I would expect “In the first step…” to be the more common of the two you offer but using the indefinite article instead is hardly incorrect.

Answer 2

In your example "as a first step" would be used. However Google ngram shows that "as a second step" is much less common; I would suggest "secondly" or some other alternative for stage 2.

Note that "In the first step we do A" does not always mean that doing A is the first step, while "As the first step we do A" does. It can mean part of the first step, or a result of the first step. So we might have

As a first step we will drive from Melbourne to Sydney. Secondly we will continue to Brisbane. In the first step we will use 80 litres of petrol, and in the second step we will use another 60 litres.