Sometimes language chance attracts great discussion — because, like, reasons. Other times it attracts no discussion, and happens seemingly for no reason. A few days ago, I encountered either late in December or in late December, I can’t remember which way round, but that doesn’t affect the point of this post. I wondered whether I should change it to the other way round. I checked Google Ngrams, but before I tell you what that showed, take a moment to think about what you would say or write, and what change has happened in the past 100 years.
Historically, the form late in [month] was the most common. It peaked in the early 1940s, then has declined in use since then. adj + prep + noun is certainly grammatical: Monday’s and Wednesday’s children are fair of face and have far to go respectively. On the other hand, in late [month] basically wasn’t used until the 1880s, then experienced a huge increase from about 1930, and overtook late in [month] between 1950 and 1960. prep + adj + noun is even more certainly grammatical.
Early in [month] and in early [month] show a broadly similar pattern, except that early in [month] was historically even stronger, while in early [month] didn’t experience as strong in increase in the 1930s and didn’t overtake early in [month] until the 1970s.
I you really have to or want to choose, go with the flow and use in early/late [month], especially if there’s a in mid-[month] somewhere nearby. But in early/late [month] is certainly not wrong. I kept the text I was editing the way it was.
Note that early/late in the month have to be that way. In the early month just registers on Ngrams, but absolutely no-one uses in the late month.