Question: Before the Buddha introduced nirvana and enlightenment, was there any way to escape from the cycle of birth and death? What is written in Buddhist texts?

Answer: 
Because the Buddha discovered reality as it actually is, rather than coming up with a personalised conception of what it is, the Dhamma is open and discoverable to all, whether there is a Buddha to light the path or not. 

Specifically within Buddhism there is a concept of [Pratyekabuddha-hood](https://en.m.wikipedia.org/wiki/Pratyekabuddha), which are beings who discover the Dhamma without a teacher - without a living Buddha or his message being available. They do not teach though.

The Buddha was not the inventor of the Dhamma within Buddhism, he was 'only' an expounder of the Truths and the Eightfold Path. Before him there were past Buddhas within the Tripitaka, and a future one too (Maitreya). 

Effectively the path is always discoverable and Nibbana achievable, to any individual willing to search.
According to Buddhism, there was no way to escape from *samsara* (the cycle of ignorance, craving & ego-becoming) before the Buddha. 

What is called 'Hinduism' arose after Buddhism. Before Buddhism, the main religion was called 'Brahmanism', which focused on 'Brahma' (god) & the Brahmin caste. There appears to be no evidence Brahmanism found a way to be free from 'samsara'. 

If Brahmanism actually knew of a way to be free from samsara, the word 'Buddha' is a lie & false, since the Buddha declared his discovery was something completely brand new, i.e., "never heard before". 

> 
> *This noble truth of the way leading to the cessation of suffering has been developed’: thus, bhikkhus, in regard to things unheard before,
>  there arose in me vision, knowledge, wisdom, true knowledge, and
>  light.*
> 
> 
> [*SN 56.11 The First Sermon*](https://suttacentral.net/en/sn56.11)
> 
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