It probably would not have been possible for all the Jews to have escaped. However, there were options available for those who had the resources and the willingness to accept the risks.
In those days it was still possible to buy emigration certificates to Palestine. I had asked my father to sell everything, to liquidate everything, and to leave. "I am too old, my son," he answered. "Too old to start a new life. Too old to start from scratch in some distant land"
The story does not specifically tell readers whether some of Sighet's Jews did choose to emigrate; the implication seems to be that they did not.
Elie's family missed an opportunity to escape. On the night that plans to begin transporting the Jews away from Sighet were announced, there was a knocking on a window of the ghetto house in which they were living, a window that had been sealed since it faced the part of Sighet that was outside the ghetto. Years later, Wiesel learned that "an inspector of the Hungarian police, a friend of my father's" was the person knocking at the window. He may have been able to help them flee if they had responded promptly.
After the family was moved again, into the smaller ghetto, their former familly maid visited the Wiesels and "begged us to come with her to her village where she had prepared a safe shelter." Elie's father refused to leave but said that Elie and his older sister could go if they wanted. Elie and his sister "refused to be separated."