I think there’s evidence on both sides and it depends how you weigh the evidence. It’s a bit like the “did grandpa wear a hat?” question. There are photos of grandpa from the 1960s and he’s not wearing a hat in any of the photos, but unfortunately there are no photos of grandpa from the 1930s when he was a young man. Did grandpa wear a hat in the 1930s? Since there are no photos of grandpa wearing a hat you could say “there is no evidence” that he ever wore a hat. But we have plenty of photos of other young men in the 1930s and it seems that they routinely wore hats in that period. You can either dig your heels in and say there is no evidence grandpa ever wore a hat, or you can acknowledge that, while there are no photos of grandpa wearing a hat, men in the 1930s generally did wear hats, and there’s lots of evidence for that, and so it’s reasonable to draw the conclusion that it’s more likely than not that grandpa wore a hat in the 1930s, even if there are no actual photos of him ever wearing a hat.
Similarly, there may not be any New Testament manuscripts with the divine name, but we do know that the divine name was used in Bible texts at the time when the New Testament was written. So it does seem reasonable to draw the conclusion that the New Testament authors would have followed contemporary practice and included the divine name in their texts.
That’s just the starting point. Corroborating that conclusion I would argue that the large number of variants around instances of kyrios in the New Testament, plus the fact that a lot of passages make better sense with the divine name included, add support to the idea that the divine name was in the original. The best example of this is the frequent quotation of Psalm 110 in the NT that probably originally read, “Jehovah said to my Lord, sit at my right hand”, that later led to the confusing rendering when the divine name was removed: “The Lord said to my lord, sit at my right hand”.