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The phrase "by first" is correct and can be used in written English.
It means "before anything else" or "before any other consideration", depending on context. For example: "We must make sure the safety of our customers by first."
Exact(52)
Predeceased by first wife Marion.
Some I know only by first name.
Students call teachers by first names.
Preceded in death by first wife, Elaine.
Neighbors greeted one another by first names.
Badly, by first sight.
Similar(5)
Osteria Dante does particularly well by first-course fish.
By first-half onslaught or last-minute defensive stand.
All redox reactions were characterized by first-order kinetics.
Here, MoS2 NTs are comprehensively studied by first-principles calculations.
All contracts are awarded by first-price sealed-bid auctions.
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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