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 Theravada tradition, Buddhas come and go over countless eons. Only in the times when their teaching is alive and true will we get a chance of escaping from this endless samsara. Every once in a great while, after a long period of spiritual darkness blankets the world, an individual is eventually born who, through his own efforts, rediscovers the long-forgotten path to Awakening and liberates himself once and for all from the long round of rebirth, thereby becoming an arahant ("worthy one," one who has fully realized Awakening). 

In Digha Nikáya Sutta 14, [Mahapadana Sutta (The Great Discourse on the Lineage)](http://buddhasutra.com/files/mahapadana_sutta.htm)) & DN 32 The Ātaānātiiya Discourse, the Supreme Buddha stated that six Supreme Buddhas appeared over 91 world-cycles. The seven Buddhas, including "our" Supreme Buddha, mentioned in DN 14 & DN 32: Vipassi, Sikhi, Vessabhu, Kakusandha, Konagamana, Kassapa, and Gotama. They were all born in this earth, in the land of the Rose Apple (Jambudipa), in north-central India in the area known then as the Middle Land (Majjhima Desa).

If such a being lacks the requisite development of a Supreme Buddha, he is unable to articulate his discovery to others and is known as a "Silent" or "Private" Buddha (paccekabuddha). These silent Buddhas come to pass a few hundred years prior to a birth of a Supreme Buddha. These Silent Buddhas too are born only in the land of the Rose Apple (Jambudipa), in north-central India in the area known then as the Middle Land (Majjhima Desa). This is a Dharmatha - a set of natural laws.

Only at a time when the Dhamma of a Supreme Buddha is alive in the world will arahants walk this earth because they require a Buddha to show them the way to Awakening. (All Buddhas and paccekabuddhas are arahants) No matter how far and wide the sasana spreads, sooner or later it succumbs to the inexorable law of anicca (impermanence), and fades from memory. The world descends again into darkness, and the eons-long cycle repeats. The most recent Buddha was born Siddhattha Gotama in India in the sixth century BCE. He is the one we usually mean when we refer to "The Buddha." 

The next Buddha due to appear is said to be Maitreya (Metteyya), a bodhisatta currently residing in the Tusita heavens. Legend has it that at some time in the far distant future, once the teachings of the current Buddha have long been forgotten, he will be reborn as a human being, rediscover the Four Noble Truths, and teach the Noble Eightfold Path once again. His name is mentioned only once in the entire Tipitaka, in the Cakkavatti-Sihanada Sutta (DN 26; The Lion's Roar on the Turning of the Wheel):

> 
> [The Buddha:] And in that time of the people with an eighty-thousand-year life-span, there will arise in the world a Blessed Lord, an arahant fully enlightened Buddha named Metteyya, endowed with wisdom and conduct, a Well-farer, Knower of the worlds, incomparable Trainer of men to be tamed, Teacher of gods and humans, enlightened and blessed, just as I am now.
> 
> 
>