What was the first board game invented? Who invented it and when?

The Royal Game of Ur is the first board game. It originated in Mesopotamia around 4,600 years ago. It's so old that I don't think the inventor is known.

There are a number of games that have been played for over 5,000 years - meaning that we know of them from archaeological evidence. So which one has been played the longest is a matter of dispute. We also do not know whether the way the game was played then is the same as the way it is played now, for those that are still played.

According to this site, the one with the earliest known evidence is Senet, a game played in Egypt at least by 3500 BCE. Next on their list is Checkers/Draughts, known to have been played in Ur (modern Iraq) by about 3000 BCE. Then, in order from earliest evidence to latest, come Backgammon (from Persia), Mehen (from Egypt), Royal Game of Ur (amazingly, from Iraq), Go (Chinese), and Nine Men's Morris (possibly Egyptian, played in ancient Rome). Chess (from India and/or China, dating from the first century CE) is a relative newcomer.

https://www.oldest.org/entertainment/board-games/