When was Hamlet written?

Because all of William Shakespeare's texts are now over four hundred years old, it is often difficult to cite an exact date for the writing of his plays. Most credible sources, such as the online edition of the Encyclopedia Britannica, locate the writing of Shakespeare's tragedy Hamlet, Prince of Denmark somewhere between 1599–1601. Various other sources cite the first performance as occurring in 1600 or 1601. It was performed by the Lord Chamberlain's Men, and because of the dates attributed to the earliest performances, these sources more specifically suggest that the writing of the play itself was completed in early 1600. Additionally, the title role was first played by Richard Burbage, a friend of William Shakespeare and one of the most famous actors to ever play at Shakespeare's famous Globe Theater. All of these factors allow us to make an educated guess and say that the play was probably completed in 1600.
https://www.britannica.com/topic/Hamlet-by-Shakespeare