The first part of the Henrician trilogy may not have been written first or been the first to be performed.

Wikipedia Chronology
First official record: possibly in Philip Henslowe's diary. On 3 March 1592, Henslowe reports seeing a new play entitled Harey Vj (i.e. Henry VI) which could be a reference to 1 Henry VI. An entry is found in the Stationers' Register in September, 1598 which refers to "The first and Second parte of Henry VJ". Most critics, however, feel this probably refers to what we today call 2 Henry VI and 3 Henry VI, not 1 Henry VI. The first definite record of the play was not until the First Folio in 1623.
First publishedFirst Folio (1623)
First recorded performance: possibly on 3 March 1592 at The Rose in Southwark, as seen by Philip Henslowe; earliest definite performance was on 13 March 1738 at Covent Garden in what seems to have been a stand-alone performance.
Evidence: On 3 March 1592, Philip Henslowe saw a new play entitled Harey Vj, but gives no further information. In August, Thomas Nashe published Piers Penniless his Supplication to the Devil, in which he refers to a play he had recently seen featuring a rousing depiction of Lord Talbot, a major character in 1 Henry VI. Most critics take Nashe's reference to Talbot as proof that the play Henslowe saw was 1 Henry VI. As such, to have been a new play in March 1592, it was most likely written some time in 1591. Furthermore, many critics consider 1 Henry VI to have been written as a prequel to the successful two-part play The Contention and True Tragedy.
Full text of play