As a short response one may say the following brief points,
Firstly: Al-Bukhaari wasn’t the first to record hadeeth. However, he rahimahullah merely collected them and chose to make a specific compilation for the authentic narrations only.
Secondly: Hadeeth was being recorded even from the time of the Prophet, sallahu alayhi wa salam, as comes reports concerning the scrolls of Ali bin Abi Taalib and as well that the Sahaabi Abdullah bin Amr bin Al-‘Aas used to record hadiths in the time of the Prophet, sallahu alayhi wa salam. For this reason we find books now from some of the second and third generations of their journals which they recorded by way of them ahadith some referred as صحيفة فلان, كتاب فلان.
Thirdly: The compilation of al-Bukhaari couldn’t be made up since there was no possible way for him to meet the exactness of other narrations and routes that were conveyed by other scholars of hadeeth who there was no means possible for al-Imam al-Bukhaari rahimahullah to collaborate with.
Fourthly: We say to those criticizing: was your scriptures recorded during the lifetime of your Prophets?
Fifthly: The fact that these ahadith are precisely memorized from one century to another shows the same possibility that they could be passed on from the generation of Prophet, sallahu alayhi wa salam, to the generations after Him. And add to that everything is documented to the extent even the biographies of the narrators are recorded let alone the hadeeths they are sharing.
AbdulFattaah Bin Uthman