Religious life started directly from the persecutions. The earliest "radicals" in following Christ died for him. They didn't exactly go out a decide to do it - those who hated the faith presented them with the option to deny Christ or die - and so they died.
Martyrdom is a grace, and a choice, but it is not something we go looking for.
And so it was with the beginning of the monastic life.
St. Paul of Thebes held to the Christian faith. To avoid the persecution, he fled to his sister's summer villa remote from Thebes - but discovered that his brother-in-law intended to turn him over to the authorities. He left there, and found a quiet, and hidden, "cave". (It was not so much a cave as a sealed valley, I think, accessed by a very narrow opening.)
And so he lived - for a very long time. He prayed, he worked the land for his food, he lived a solitary life dedicated to God. He lived to 113 years, according to St. Jerome.
Near the end of his life, Anthony (who would become St. Anthony of Egypt) visited Paul, to ask him about the spiritual life and the life of solitude. St. Anthony later returned and buried the old hermit.
It was the beginning - and, in God's providence, it just sort of "happened" through circumstances and the fidelity of one man to his faith. Others later sought out the lifestyle and the Fathers of the Desert learned (and taught) much about the life of the Spirit and intimacy with God. Even now, they teach us to be humble, silent and diligent in our labor. They speak of ascetic labor, its great good and its pitfalls. They can lead a soul to God.
And they were the beginning of a form of life that has continued through the centuries, blossoming into myriad forms and assisting the life of the Church even till today.