Fibonacci Numbers were first discovered by Indians in 200 BC.

Fibonacci Numbers are part of Nature. They are part of advance science followed by Nature.

But the credit goes to Fibonacci who also learnt about Indian Decimal System and introduced to Europe.  So being introduced to something so basic, how come one can advanced to these numbers so soon?

Apparently this was known to Indians as early as 200 BC.  It was called Virhanka numbers.

https://en.wikipedia.org/wiki/Virahanka

Susantha Goonatilake writes that the development of the Fibonacci sequence "is attributed in part to Pingala (200 BC), later being associated with Virahanka (c. 700 AD), Gopāla (c. 1135), and Hemachandra (c. 1150)".[7] Parmanand Singh cites Pingala's cryptic formula misrau cha ("the two are mixed") and cites scholars who interpret it in context as saying that the cases for m beats (Fm+1) is obtained by adding a [S] to Fm cases and [L] to the Fm−1 cases. He dates Pingala before 450 BC.[14]

However, the clearest exposition of the sequence arises in the work of Virahanka (c. 700 AD), whose own work is lost, but is available in a quotation by Gopala (c. 1135):

Variations of two earlier meters [is the variation]... For example, for [a meter of length] four, variations of meters of two [and] three being mixed, five happens. [works out examples 8, 13, 21]... In this way, the process should be followed in all mātrā-vṛttas [prosodic combinations].[15]

The sequence is also discussed by Gopala (before 1135 AD) and by the Jain scholar Hemachandra (c. 1150).