The question of whether we would exist if time travel existed is a complex one, and it depends on the specific rules and implications of time travel in the hypothetical scenario. Different fictional works and theories propose different concepts of time travel, and their consequences can vary.
Self-consistency principle: One theory, often seen in science fiction, is that time travel is subject to the self-consistency principle. According to this principle, any actions performed in the past would already be accounted for in the present. In other words, if time travel were possible, any changes made in the past would have already influenced the present, and there would be no significant alterations to the course of events. Under this principle, it's possible that we would still exist, but any attempts to change the past might be futile or lead to unintended consequences.
Alternative timelines: Another popular concept is that time travel creates alternate timelines or parallel universes. According to this idea, traveling back in time could create a separate timeline, branching off from the original one. In this case, any changes made in the past would affect the alternate timeline but not necessarily the original timeline from which the traveler originated. So, in this scenario, we would still exist in our own timeline, while alternate versions of events unfold in other timelines.
Predestination and determinism: Some theories of time travel suggest that the past, present, and future are all predetermined and interconnected. In such a model, time travelers would be unable to change anything because their actions were already part of the timeline. From this perspective, the existence of time travel would not fundamentally alter our existence since everything would already be accounted for in the predetermined sequence of events.
It's important to remember that time travel is purely speculative at present, and we don't have any definitive scientific evidence or practical implementation of it. The hypothetical implications of time travel are still a subject of ongoing exploration, discussion, and creative interpretation.