Sure, inasmuch as concepts require conscious minds. But surely the universe would exist if it had never spawned conscious observers. So I don't see that the question of existence begins and ends with conscious observers.

It has to begin and end with conscious observers, because they are the only ones that can consider the question. The universe does not need your answer, you do. The question quite literally ends when you do.

Why? Did universe not exist before the first life appeared?

The meaning of the word "exist" implies that it has some way to be detected by conscious observers.

Consider this: if I tell you there about a parallel universe you can never detect or discover, how does saying "BUT IT EXISTS" differ from saying "GOT YOU, IT DOESNT EXIST"?

I get your hypothetical example, however, will the universe cease to exist after the last conscious observer dies? For that observer, one minute before their death, would/should they suppose that universe will cease to exist or continue existing?

If we humans manage to wipe out ourselves next year in a nuclear holocaust, then is the continued existence of our planet conditional on some other conscious life arising in the future? Obviously it continues to exist even in your definition because they would be able to observe it, but how could such life arise if the universe doesn't exist?

I'd rather define "exist" as having an effect on our physical reality, which would obviously be detectable by "observers" in e.g. the quantum mechanic meaning of "observation" that has no relation to consciousness.

You're focusing too hard on the "existence" part and not hard enough on the "thing" part.

If humanity died tomorrow, nobody would be around to call the planet "Earth". Earth is merely a concept held in the minds of people. The concept consists of properties, only some of which involve the physical aspects. For example, lots of other planets are physically present, but only one we call Earth, because we live on it. Should we not live on it anymore, why would anyone bother to call it by a name.

In that sense, sure, Earth would cease to exist if we stopped living on it.

The problem with defining existence as only involving the physical is that it yields a world in which nobody can make sense of anything. You can't simply boil everything down like that and actually live in that world. The very second you started thinking, you'd start ascribing properties to objects that aren't merely physical, recreating the entire debate.

Before you consider existence, think about what "thing" means.

You said it yourself: "having an effect on our physical reality". It is a binary relation: something exists because we can experience it or deduce it from other things we experience.

In your hypothetical example, the existence a planet after it has eg exited our visible universe (because of the rapid expansion of the universe) is only relevant to us because we were able to deduce it from previous observations. Same with things in the past. So to answer your question, since we observe the Earth now, we can deduce its continued existence even after a cataclysm that would wipe out all life on Earth. We could be wrong in our extrapolation. Maybe the Earth would be hit by an asteroid later and things would be different in a way no one imagined. But, without conscious observers at that point, that state of affairs would be not unlike physics in that parallel universe. In that case, according to your definition, it wouldn't exist.