I'm no grammarian, but my instinct here is to use "at". I think "at" works better with something that is an event, something that is scheduled to happen on a certain day. If we were talking about a period of time, "in" would work, but so would "at": "Experts predict the economy will take a downturn in the beginning of 2021." (I typed that example using "in" and this bothersome grammar bot flagged "in" and recommended "at"! Curses. I stand by my instinct. ) We always use "in" and never "at" when talking about a season: "I will be taking an economics class in the spring." Or when referring to a month: "The winds will return in September."
In English, the phrase "in the beginning" has a powerful resonance, because it is the opening phrase of the King James translation of the Bible. For that reason, I think we are sometimes drawn to that wording, especially if we want to lend some gravitas to the subject: "In the beginning, the company was a struggling start-up working from Steve's garage in Silicon Valley."