How old was Buddhism/Shinto before Shinto began to adopt aspects of Buddhism 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.[1][10] 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.[1][11][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 &quot;pre-history&quot; that &quot;significantly&quot; 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



And,

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.

And,

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 &quot;prehistoric Shinto&quot; 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.