This is an interesting question and, often, the first answer automatically thought about might be the location of Shakespeare's birthplace next to the Forest of Arden in England, which is often thought of as an obvious predecessor to the As You Like It Forest of Arden. Yet there may be more in Shakespeare's socio-political background that is relevant to As You Like It. In the in-depth essay "The Forest of Arden in Our Minds: ... and what it meant to the author and his contemporaries" by Britta Calamnius of Gotland College, Sweden, the relevance of this element of background is explored with interesting results.
Calamnius points out that it was a living reality that nobility were fleeing Elizabeth's court and escaping to the safety of the remote countryside, including remote forests. This flight was triggered by the violent schism between Catholic and Protestant powers and beliefs in England during Elizabeth I's reign. While Protestant Elizabeth I came to the throne planning and hoping for moderate policy and religious tolerance following Catholic Queen Mary I's violent purging of Protestantism from England (which was itself avenging Henry VIII's purging of Catholicism), people took a differing view and opposed a policy of tolerance.
There were Protestant factions that wanted bloody revenge for the bloody attacks of Mary I, and there were Catholic factions that wanted the restoration of the supremacy of Catholicism (especially after Pope Pius VI excommunicated Elizabeth) and the reinstatement of nobles who had been deposed from positions of leadership when the reign changed from Mary I to Elizabeth I. In addition to which, there were plots brewing amongst the nobility and being orchestrated by the Vatican to have Elizabeth assassinated. In the midst of this turmoil, nobels were fleeing for their lives away from court to remotes areas since some punishments for religious-political disloyalty called for execution, just as courtiers fled from Duke Frederick to Arden:
They say he is already in the forest of Arden, and a many merry men with him; and there they live like the old Robin Hood of England: they say many young gentlemen flock to him every day, and fleet the time carelessly, as they did in the golden world. (As You Like It, I.i)
Two examples of this pointed out by Calamnius are the execution for religious-political activity of a relative of Shakespeare's and the execution of the Earl of Essex. Calamnius's brief comment on the first is:
Even a relative of Shakespeare’s was beheaded and got
his head shown at The Tower Bridge, for religious-political
Another example is the fate of the Earl of Essex. Essex was engaged with one of Shakespeare's theatrical patrons, the Earl of Southampton, in plotting the assassination of Elizabeth. The plot failed; they were imprisoned; Essex was beheaded
His friend and patron, the earl of Southampton, was planning a revolt against the queen soon after, together with the earl of Essex and others. They were imprisoned, and Essex was beheaded,.... (Calamnius)
Sir Walter Raleigh is another noble who was imprisoned, more than once, then eventually beheaded. This social and political turmoil is certainly part of Shakespeare's background and, according to scholars, is certainly relevant to As You Like It as reflected by the flight of nobility and courtiers from a tumultuous court to the peaceful and gentle countryside Forest of Arden.