If there are alien races billions of light years away from us and they have a similar technological level to ours, it is highly unlikely that they would know we existed. Here's why:
Speed of Light Limit: The speed of light is the fastest speed at which information can travel in the universe according to our current understanding of physics. Since these hypothetical alien races are billions of light years away, it would take billions of years for any signal or information from Earth to reach them. Similarly, any signals or information they send would take billions of years to reach us. This vast distance makes direct communication or knowledge exchange extremely difficult.
Detection Challenges: Even if we assume that these alien races have advanced technology, detecting the existence of Earth and its inhabitants from such a tremendous distance poses significant challenges. Our radio signals, for example, weaken as they travel through space and would become extremely faint and indistinguishable from background noise over such vast distances. Additionally, the sheer number of stars and planets in the universe makes pinpointing the existence of Earth a daunting task.
Temporal Misalignment: Due to the time it takes for light to travel, any information received by these hypothetical alien races would be billions of years old. They would be observing Earth as it existed billions of years ago, and they would have no knowledge of our current technological level or any recent developments. Similarly, any information we receive from them would be billions of years outdated, reflecting their past state of advancement.
It's important to note that the hypothetical scenario of alien races at a similar technological level billions of light years away is purely speculative. While there is a possibility of extraterrestrial life in the universe, we currently have no direct evidence or contact with such civilizations. Our understanding of the vastness of the universe and the limitations imposed by the speed of light suggests that the chances of mutual knowledge or communication between distant civilizations at our level of technology are extremely remote.