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The phrase "at first we understood" is correct and usable in written English.
It can be used to indicate an initial comprehension of a situation or concept that may change later on.
Example: "At first we understood the project requirements clearly, but as we delved deeper, we realized there were many complexities we hadn't anticipated."
Alternatives: "initially we grasped" or "in the beginning we comprehended".
Exact(1)
At first, we understood and specified the context of use by Persona.
Similar(59)
At first, we understand.
"At first we did not understand the importance of bringing children to this centre.
At first, we did not really understand why we were discussing this term.
For these researches, at first we have to clearly understand the terminology behind it.
At first we thought it had been understood and would be used, but….
I don't think at first they understood what we were trying to do.
"At first everyone understood, but how long are they going to take?" said Andy Berger of Cornwall-on-Hudson, an avid reservoir fisherman.
At first, Reichek understood her technique as drawing with thread, not sewing.
These bumps make us see the value of the discovery.' And in §464: 'My aim is: to teach you to pass from a piece of disguised nonsense to something that is patent nonsense.' In the discussion of the possibility of a private language it may well at first seem as though we understand the possibility under consideration.
In the beginning, the results were sometimes disappointing, but this was because it was not at first understood that not only diseased trees but all elm wood in which the beetles might breed must be destroyed.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com