> Could we let other apes and animals evolve over millions of years under our supervision and eye?

I think we must assume we cannot. There hasn't been any major civilization that has been around for more than a few hundred or thousands of years.

If we construct such a project in a way that it has a 0.01% chance to crumble in a single year (which is why lower than anything our society can achieve right now), there's about a 10% chance it fails within 10k years, a 63% chance it fails in 100k years, and a 99.995% chance it fails within a million years.

Given enough advancements in computer science we could simulate millions years of apes evolution within a span of days or hours and observe the results. Which is the basis of the argument for simulation hypothesis [1]

[1] https://en.wikipedia.org/wiki/Simulation_hypothesis

That's basically the premise of the Uplift series by David Brin.

The premise of that series is that except for the original species, there had always been intervention to uplift not just observation. Humans had been a bit of a surprise because they had no apparent uplifters. IIRC the general viewpoint was that self-evolution in this way was just not possible so there must have been some kind of deception involved.

isn't that the main loop hole of who was born first? chicken or the egg?

Egg was first by millions of years.

Do you mean "cell" which is neither egg (which is a specific specialized kind of a cell - reproductive) nor chicken?

Well, the cellular specialization arose long before amphibians emerged from bodies of water, and amphibians laid eggs long before birds evolved, eventually branching out into any species of chicken.