No, it is not possible for Earth to escape our solar system under normal circumstances. The solar system is gravitationally bound, meaning that the objects within it, including the Sun, planets, and other celestial bodies, are held in orbit by the Sun's gravitational pull.
In order for Earth to escape the gravitational influence of the Sun and leave the solar system, it would require an enormous amount of energy. This energy would need to overcome the gravitational pull of the Sun and the gravitational interactions with other planets and objects in the solar system.
Currently, our space exploration capabilities are limited to sending spacecraft to other planets within our solar system. While humans have sent several robotic missions to explore other worlds, such as Mars, Venus, and beyond, the energy requirements and technological challenges for sending a human-made object, such as Earth, out of the solar system are currently beyond our reach.
That being said, it's worth noting that in about 5 billion years, the Sun will enter the red giant phase of its evolution and expand, eventually engulfing the inner planets, including Earth. But this scenario is not Earth escaping the solar system but rather a consequence of stellar evolution.