There has been discovery of several hadith texts belonging to the 1st Century Hijrah (Islamic year) whose contents were compared by modern Muslim & Non-Muslim scholars and researchers, with the canonical collections of the 3rd century Hijrah (9th century CE) of Imam Bukhari, Imam Muslim, Imam Ahmad etc. Their findings reveal that the hadith were almost identical with no issues. Among those that were subject to such research in the recent years in particular were Sahihfa (scriptures) of Hamam ibn Munabbih and Musannaf of Abdul Razzaq of the 1st Century. Below are some of their findings which support the fact that not only were hadith being collected in the first century but also their authenticity has been proven to be correct.
Sahifah (Scripture of) Hamam Ibn Munabbih
Sahifah (Scripture of) Hammam ibn Munabbih (d. 101 AH) is perhaps one of the earliest known hadith collections, by 8th century scholar Hammam ibn Munabbih. It has been translated in the 20th century by Muhammad Hamidullah - a world-renowned Muhaddith, Faqih and scholar of Islam and International Law from Pakistan, winner of national award Hilal-e-Imtiaz in Pakistan. Hammam ibn Munabbih was the taba'een (student) of the Companion, Abu Huraira (r.a), the famous hadith transmitter. Dr Hamidullah published this Sahifa of Hammam around 1979 and it proves that hadith were collected in the Mid 1st century Hijrah. His research was also compared by orientalists such as, by R. M. Speight who mentions that: “… the texts in Hammam and those recorded in Ibn Hanbal, Bukhari and Muslim with the same isnad show almost complete identity, except for a few omissions and interpolations which do not affect the sense of the reports. On the other hand, the same ahadith as told by other transmitters in the three collections studied show a rich variety of wording, again without changing the meaning of the reports.”  Speight shared his analysis after comparing it (i.e., the Sahifa) with about the 1500 variant readings of the same ahadith found in the collections of Ibn Hanbal (Musnad), al-Bukhari (Sahih) and Muslim (Sahih); dating from 3rd Century Hijrah.
Musannaf Abdul Razzaq
Another book from the 1st century belonging to the famous early Muslim Muhaddith (hadith expert and teacher) named Abdul Razzaq Sanani (124 AH - 211 AH) was studied by another Western Non-Muslim writer name Harald Motzki. His analysis appeared in the Journal of Near Eastern Studies and he says that: “The works of ‘Abd al-Razzak are extremely important for the study of early Islamic jurisprudence, hadith and exegesis of the Kur’an because they contain older sources or materials which have otherwise been lost. ‘Abd al-Razzak had direct access to authors of the first extensive compilations of traditions arranged according to subject . . . like those by Ma’mar b. Rashid, Ibn Djuraydj, Sufyan al-Thawri and Sufyan b. ‘Uyayna. His own Musannaf is to a large extent compiled from materials received from these four scholars, and it is very probable that these materials came for the most part from their books. In general, ‘Abd al-Razzak’s transmission from these teachers of his seems to be reliable . . . While studying the Musannaf of `Abd al-Razzaq, I came to the conclusion that the theory championed by Goldziher, Schacht, and in their footsteps, many others - myself included - which in general, reject hadith literature as a historically reliable sources for the first century AH, deprives the historical study of early Islam of an important and a useful type of source.” 
Even though as Muslim Believers we do not need the above findings to prove us the authenticity of the hadith literature, yet this confirms for us even more that the hadith of the Prophet ﷺ were collected through a science called ilm Al hadith which no doubt was an effective methodology and has produced for us results that helped Muslims guided for the past 14 centuries.
 R. M. Speight, “A Look At Variant Readings In The Hadith”, Der Islam, 2000, Band 77, Heft 1, p. 170 https://www.islamic-awareness.org/hadith/hadith
 H. Motzki, “al-Sanani, Abd al-Razzak b. Hammam b. Nafi, Abu Bakr al-Yamani al Himyari (IX 7a)”, in Encyclopaedia of Islam CD-ROM Edition v. 1.0