JS obtained the plates in 1827 and commenced translating them then.
Joseph Smith, Jr. “A History of the life of Joseph Smith Jr.," [ca. June 1832], 5, The Joseph Smith Papers website, accessed July 16, 2021
therefore I was chastened and saught diligently to obtain the plates and obtained them not untill I was twenty one years of age and in this year I was married to Emma Hale Daughtr of Isaach [Isaac] Hale who lived in Harmony Susquehan[n]a County Pensylvania on the 18th January AD, 1827, on the 22d day of Sept of this same year I obtained the plat[e]s—and the in December following we mooved to Susquehana by the assistence of a man by the name of Martin Har[r]is who became convinced of th[e] vision and gave me fifty Dollars to bare my expences and because of his faith and this rightheous deed the Lord appeared unto him in a vision and shewed unto him his marvilous work which he was about to do and <h[e]> imediately came to Suquehannah and said the Lord had shown him that he must go to new York City <with> some of the characters so we proceeded to coppy some of them and he took his Journy to the Eastern Cittys and to the Learned <saying> read this I pray thee and the learned said I cannot but if he would bring the blates [plates] they would read it but the Lord had forbid it and he returned to me and gave them to <me <to> translate and I said I said cannot for I am not learned but the Lord had prepared spectticke spectacles for to read the Book therefore I commenced translating the characters
Joseph Smith received the plates in 1827 at age twenty-one, but Martin Harris lost the manuscript that was translated at this time, which leaves the translation Book of Mormon as we know it occurring at a later date.