"first object" is correct and usable in written English.
You can use it when referring to the first item in a sequence of objects. For example, "John grabbed the first object in the row."
Photograph: /AMSA The first object possibly associated with flight MH370.
The first object was to explore the Rongbuk valley.
Insult on injury, the first object she saw upon entering the apartment was my tub.
"That was the first object that didn't quite fit any of the existing categories".
The face, psychoanalysts consider, is the first object to acquire visual meaning and significance.
In 1758 it was the first object listed (M1) in Charles Messier's catalog of nebulous objects.
Trickledown cruelty is the first object lesson in the cutthroat world of Ms. Headland's play.
Indeed, it was the first object that Chandra took a picture of.
Getting the water to flow again was the first object of the Mosses' restoration programme.
Hence, Gliese 229 B was the first object widely accepted as a brown dwarf.
