If there were no other planets or stars in the universe, and assuming Earth remained the only massive object, the concept of escape velocity would still apply. Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a celestial body and not fall back.
In the scenario you described, if an object were launched from Earth's surface with a speed greater than the escape velocity, it would indeed overcome Earth's gravity and continue moving away indefinitely. On the other hand, if the object's speed were below the escape velocity, it would eventually succumb to Earth's gravitational attraction and return.
The escape velocity depends on the mass and radius of the celestial body from which the object is launched. For Earth, with its mass of approximately 5.97 x 10^24 kilograms and radius of approximately 6,371 kilometers, the escape velocity is about 11.2 kilometers per second (or approximately 40,270 kilometers per hour or 25,020 miles per hour).
So, in the absence of other celestial bodies, an object would need to reach or exceed a speed of about 11.2 kilometers per second to escape Earth's gravitational pull entirely and not fall back.