One of the first students to be sent away for education may have been the son of José de la Guerra y Noriega, Juan José Noriega, who was sent to Liverpool, England for education in 1825. When he returned to California in c.1831 at the age of about 21 he was tutored in higher mathematics by Father Patrick Short who in 1834 jointly with William Hartnell, who had engaged him as Noriega's tutor, founded the first school/college in California. Noriega died in 1833 but in a way his legacy, the relationship between Hartnell and Short, led directly to the foundation of the "Colegio de San Jose".
Captain John Lincoln of the ship John Begg wrote to Hartnell on the 15th July 1826 and mentioned Juan José Noriega:
https://archive.org/details/documentos12449996vall/page/n122/mode/2up
(my transcription)
You will undoubtedly be surprised at my not bringing Letters from Don Juan Noriega but having rec'd some from California a few days previous to our sailing he retook back his letters to write others which supposedly will come out by first conveyance. He certainly is a prodigy of nature in acquiring a Language he speaks the English Language fluently and has made great progress in French – he certainly has excelled some that have been in England 3 years from Peru.
Then on 19th March 1827 Juan José Noriega himself wrote to Hartnell from Liverpool and lists the subjects he is studying but doesn't say much else except that he's too busy to write to his sister!
Bancroft in his "History of California:1825-1840" refers to the above letter and states that he was later educated at the "Mont." school under Hartnell and P.Short. He includes the information that Noriega died in 1833 unmarried. In fact Bancroft is incorrect as the school was not formally founded until 1834, after Noriega's death.
Separately fromChapter 5 - 'Schoolmaster' of Dakin's "The Lives of William Hartnell" explains in detail the above, it appears from a letter sent on 10th August 1829 fromevents surrounding the return of McCullochNoriega to, the engagement of HartnellFather Patrick Short that another boy may have been sent to Lima underas his care:
https://archive.org/details/documentos2455129997vall/page/n356/mode/2up
(my transcription)
I beg leave to enclose you an account against Don Domingo Carrillo for the education of his Son Jose Antonio in Lima and which I will feel obliged by your recovering for me and by your remitting at your most early convenience. I also enclose you the copy of a letter which I have written to Don Domingo which I will feel obliged by your perusing and taking your measures accordingly; you will also find accompanying the several receipts and Documents for the various sums mentioned in the Account of Charges.
I have no more information than is in this extracttutor, so it's not possible to say what sortand the subsequent founding of education this boy receivedthe "Colegio de San Jose".