It is a common misconception amongst people that hadiths were collected and written down after 150 to 200 years of Prophet Muhammad (SallAllah-u-Alaihi-Wa-Sallam’s) death. This misconception has led to people viewing hadiths suspiciously as they surely can’t be authentic as they were collected much later.

Hadiths were compiled and written down since the time of Prophet Muhammad (SallAllah-u-Alaihi-wa-Sallam), sahaba (RadiAllahu Tala Anhum) had their own scrolls or books, with the help of these scrolls and books other hadith books were compiled later onwards.

At first the Prophet (SallAllah-u-Alaihi-wa-Sallam) stopped his companions (RadiAllahu Tala Anhum) from writing down hadiths.
[Sahih Bukhari]

Whatever the reason, then afterwards this was permitted, there is a narration regarding it but it is dhaeef so we are not writing it.

Prophet of Allah (SallAllah-u-Alaihi-wa-Sallam) said to Abdullah bin Amr (RadiAllahu Tala Anho): Write hadiths, I swear by Him who holds my life in His hand, from this mouth nothing but the truth comes out.
[Abu Dawood, volume 1, pg 158: Sanad is Sahih]

Abdullah bin Amr (RadiAllahu Tala Anho) says: We were seated near prophet of Allah (SallAllah-u-Alaihi-wa-Sallam) and were writing, in this manner was asked: which city will be first conquered, Constinople or Rome?

He (SallAllah-u-Alaihi-wa-Sallam) said: Hercule’s city will be conquered first.
[Darmi, pg 126: Sanad is Sahih]

Prophet (SallAllah-u-Alaihi-wa-Sallam) said: Write this hadith and give it to Abu shah (RadiAllahu Tala Anho)….
[Sahih Bukhari & Sahih Muslim]

Ali (RadiAllahu Tala Anho) says: We don’t have anything but Kitab Allah and the scriptures in which are hadiths of prophet of Allah (SallAllah-u-Alaihi-wa-Sallam).
[Sahih Bukhari & Sahih Muslim]

Abu Huraira (RadiAllahu Tala Anho) says: Amongst the sahaba (RadiAllahu Tala Anhum) no one narrates hadiths more than I do save Abdullah bin Amr (RadiAllahu Tala Anho), because he used to write them and I didn’t.
[Sahih Bukhari]

Anas (RadiAllahu Tala Anho) heard a hadith and liked it so much, he told his son to write it and he wrote it.
[Sahih Muslim, Kitab ul Iman]

Anas (RadiAllahu Tala Anho) says that when Abu Bakr (RadiAllahu Tala Anho) sent him to Yemen as the governor, he wrote on a scroll and gave it to him whose content was: Start with Allah ‘s name who is Rehman and Raheem, this is the obligation of Zakat which Prophet of Allah (SallAllah-u-Alaihi-wa-Sallam) has made on the Muslimeen and this is what Allah ordered His prophet
[Sahih Bukhari, Kitab ul Zakat]

The narrator Hamad bin Salma says: I got this book from Anas (RadiAllahu Tala Anho) ‘s grandson Samama.
[Nasai, kitab ul zakat]

Imam Malik says: I read Omar (RadiAllahu Tala Anho) ‘s book …
[Muwatta Malik, pg 106]

From the above few authentic narrations from many, we can conclude that Hadiths were being written down since the time of the prophet (SallAllah-u-Alaihi-wa-Sallam). From such scripts other famous hadiths books were compiled.

But where are these scrolls or books?

When the hadiths were copied and narrated into other books, it was but logical that the small compilations get absorbed in bigger compilations.

It is not true that the muhaddiths collected only verbally transmitted hadiths, and there were no compilations in the earlier times especially the first century of the hijra.

Old compilations can be found today like Sahifa Hammam, in this are hadiths in which Imam Hammam bin Munabbi took dictation from Abu Huraira (RadiAllahu Tala Anho), this compilation is easily available for everyone to view.

So to say that there were no compilations for hadiths till the second century is just a misconception spread by helpers of shaitan so that people give up believing in hadiths and interpret Quran according to their desires thus making a mockery of prophethood which is clear blasphemy. May Allah save us form such a thought. Ameen.