Shroddingers cat is about viewing a quantum particle changes the outcome, because everything we can measure with is way WAY bigger than the quantum particle. It's literally like investigating an ant with a marble, every time you touch the ant, the marble changes the properties of the ant somehow, speed, position, direction... so you can't get detailed info on the ant.

Pretty sure I read an article recently that explained quantum entanglement and it boiled down to math works different on the quantum scale, and in quantum math if you know 1 of 4 properties of a pair of entangled quantum particles, you can reason out an answer the same way we can figure out a property by knowing 3 of 4 properties. It's like trying to visualize infinity or a 4D object, our brains are not wired to conceive quantum math. It doesn't make sense because to us because it doesn't make sense in our corner of space time.

At some point 2 grains of sand stuck together that would eventually become the earth, but is that actually the earth? Before the moon was formed in an impact with another proto-planet, it was not the same size or composition as today, so at that point it was also a proto planet. That impact was the final step to those proto planets becoming the Earth and Moon, so personally I would say the earth is 4.5B years old, the point it became its final mass. (Also, the cores of the 2 proto planets would have combined at that point giving the earth a large core and powerful magnetic field).

4.543B. 543M years is plenty for an atmosphere to form. Hell, oldest known evidence of life on Earth is 3.7B.

Anyways, here is a credible source

https://forces.si.edu/atmosphere/02_02_01.html#:~:text=(4.6%20billion%20years%20ago)&text=As%20Earth%20cooled%2C%20an%20atmosphere,from%20gases%20spewed%20from%20volcanoes

Pretty sure earth has had an atmosphere of one composition or another for like 4B years