Before Shinto began to adopt aspects of Buddhism i am wondering how old the 2 were as to which of the 2 was the older. by age i am referring to from when they started to become a following and not from when their creation myths occurred.
Buddhism originates with the historical Buddha:
The times of Gautama's birth and death are uncertain. Most historians in the early 20th century dated his lifetime as circa 563 BCE to 483 BCE. More recently his death is dated later, between 411 and 400 BCE, while at a symposium on this question held in 1988, the majority of those who presented definite opinions gave dates within 20 years either side of 400 BCE for the Buddha's death.[note 4] These alternative chronologies, however, have not yet been accepted by all historians.
The historical Buddha lived in or near what is now northern India, i.e. far from Japan.
Re. the Origins of Shinto, recorded history dates to circa 700 CE (i.e. about 1000 years later than Buddhism) but archaeology shows a "pre-history" that "significantly" earlier than that:
Shinto has very ancient roots in the Japanese islands. The recorded history dates to the Kojiki (712) and Nihon Shoki (720), but archeological records date back significantly further. Both are compilations of prior oral traditions.
The BBC's short History of Shinto says,
Periods of Shinto history
One of the standard classifications of Shinto history reduces it to four major periods:
Before the arrival of Buddhism in Japan
Shinto and Buddhism together in Japan
Shinto and Buddhism together
From the 6th century CE the beliefs that are now known as Shinto were greatly altered by the addition of other ingredients.
Shintoisms were the only religions in Japan until the arrival of Buddhism in the 6th century CE. From then on Shinto faiths and traditions took on Buddhist elements, and later, Confucian ones. Some Shinto shrines became Buddhist temples, etc.
Before the arrival of Buddhism
During this period there was no formal Shinto religion, but many local cults that are nowadays grouped under the name Shinto.
Like many prehistoric people, the first inhabitants of Japan were probably animists; devoted to the spirits of nature. In their case these were the Kami that were found in plants and animals, mountains and seas, storms and earthquakes, sand and all significant natural phenomena.
The early Japanese developed rituals and stories which enabled them to make sense of their universe, by creating a spiritual and cultural world that gave them historical roots, and a way of seeming to take control of their lives, in what would otherwise have been a fearful and puzzling landscape.
Other cults that are grouped together into Shinto probably arrived in Japan from Korea with the Korean tribes which invaded Japan in late prehistoric times.
These religions were highly localised, and not organised into a single faith. Nor were they seen as a single religion; the realms of Earth and the supernatural were so closely integrated in the world-view of the early Japanese that the things that modern people regard as a faith were seen in those times as just another part of the natural world, albeit a part of enormous power.
So "prehistoric Shinto" was (as well as being pre-historic) not necessarily a single religion. As such I suspect it may be impossible to define exactly when it began.
If you want to know more about what archaeology says about the origins of pre-historic Shinto, that seems like an appropriate question to ask on the 'History.SE' site.
I belong to a one of the Guardian races (Sinhalese) of Theravada Buddhism.My country (Srilanka) was visited by Lord Buddha few times and we became Buddhists in the era of king Ashoka of India.
As we (Indian and Srilankan Monks and Buddhist societies in both countries) have now calculated and accepted Buddhism is about 2600+ years old.
Theravada is the oldest tradition of them all and this is our calculation as the Theravada Buddhists.