Is there any evidence of manistream Jews ( Where Jesus's apostles came from) using it in their writings at the time?
I am sure you know that early copies of the Septuagint contained forms of the divine name. This is the main line of evidence.
If you look at extant copies of the New Testament, then of course the testimony is unanimously in favour of kyrios rather than the divine name in the New Testament. But if you approach the question differently, and ask what was Jewish practice concerning the divine in sacred texts in greek during the first century, when the New Testament was written, you get quite a different answer. The extant manuscript evidence is decidedly in favour of the view that first century Jews used forms of the divine name instead of Greek substitutes.
Plus the text of the New Testament itself provides evidence that the divine name stood in the original. For example Psalm 110:1 is quoted in reference to Jesus more than any other OT text. Yet in the Greek text as it survives it is quoted as saying:
"'The Lord said to my Lord: "Sit at my right hand until I put your enemies under your feet."'
That awkward ambiguity would not have existed for first century Jews who read either in their Hebrew or in their Greek copies a clear distinction between YHWH and their Lord Jesus. The fact that Christians found the text unproblematic and used it so freely in the first century is good evidence that the ambiguity between the two Lords in this passage had not yet been created by the substitution of YHWH with kyrios.