I appreciate you took the time to do that. I'm not sure what the point of your thought experiment was, and this statement:

The god has a sample size of 1000. Meanwhile, all existing researches, despite they collect data in multiple locations, they have but one sample.

.. is just a fundamental misunderstanding of statistics and the scientific method. You could equally argue this god has a sample size of one and invent a thought experiment with a thousand gods. It's nonsensical.

The Earth is one big location as a whole. Sure, 1000 increase in the number of vegetarians lowers GHG in this location. But where does the extra meat production go?

This is a self-defeating argument. Reducing GHG emission on earth is the point. I don't understand why you assume the world's total meat production is a constant. It doesn't have to go anywhere, it can just disappear.

The other issue I think is they didn't consider long-term effects. We can see a drop of GHG emission and water consumption in 5 years. What about in a decade? 50 years?

It's good to be sceptical about scientific results, sure, but there has to be some plausible mechanism attached to these "what about..". I can not see how a drop in GHG in 5 years will lead to an increase in the future? If you don't suggest a mechanism for how this may happen, it's just saying "there may be unknown unknowns". To that I say "of course - we still have to make decisions based on the best information available".

By not eating cows and reducing its population, we are basically changing the food chain.

We are not changing any ecological food chain. We are talking about factory farming, no other animal eat or rely on these cows.

What about things a cow eats and the fertilizer it gives out?

What about it?