However, it does seem to often that things just work out in a manner that is too predictable to simply be random chance. Then again, evolution would also explain some of the predictability.
That's a psychological phenomenon that is common in all kinds of animals, not just humans. It's called confirmation bias. We notice the things that make sense and ignore the things that don't. From an evolutionary standpoint, we have evolved to find patterns and we are so good at that that we find patterns in places where they simply don't exists. We recognize this :) as a smiling face for a very similar reason.
I don't know that anyone can say with certainty that the concept of a "higher power" is false
Generally speaking, proving something doesn't exists is not something you can do. You can not prove that lepricaunts don't exists, you cannot prove that ferries don't exists, you cannot prove that unicorns don't exists and you cannot prove that the flying spaghetti monster doesn't exist. But with all of those things, the right question in my opinion is not if they exists, but if it is rational to assume they do. I think that a belief that is accepted without evidence is simply not rational. You might not be able to confirm with 100% certainly that a higher power does not exists, but it is not rational to assume it does in the absence of any evidence to support that.
When we do, we would be the "higher power" who designed the new life and the systems in which they exist - could this not be our reality today?
Many contradicting things could be true. That's why we should not assume any of them until we have evidence that would help me determine which if any of the options we might be aware of is likely. Otherwise, chances are we would be assuming the wrong thing.
If we create life, would we really be the higher power that you are otherwise describing?
And another question. You say you believe in a higher power. What are its attributes in your view?
RE: Australia shedding religion from their culture, "No Religion" is now primary belief.