Our perception, reason, experience & knowledge are very limited. We can only say a thing doesn't exist if it is absent from those things, but just because a thing is absent from our awareness doesn't mean it doesn't, or can't, exist. So we can never conclusively prove non existence.

The best we can hope for is probability. We can say it is highly unlikely something exists, but in our limited state, we can never prove it conclusively, The perception that something is absent only proves it is absent, not that it doesn't exist.

We also come to the problem of definition. Definitions of "god" are all over the map. It appears to be a concept without content, so proving if it exists or doesn't is a moot point, for something to exist or not exist, it must be a "something"

Only by proving that the circumstances and environment necessary for its existence do not exist.

It depends on the circumstances and the definition of "something". For example if that thing is a political claim by a dishonest politician who says that an unprecedented "crisis" exists on the U.S. southern border to justify an expensive wall, but we suspect this "crisis" does not exist due to the proven history of dishonesty from that politician, then we can prove the "crisis" does not exist by comparing past and present immigration data.

[pewresearch.org]

It is so much in the nature of our language that we can talk about things the do not exist outside of our imagination or belief in their existence.

Not always like God

If it doesn't exist as you say, how do you know that? Why prove something doesn't exist when in your very question you state it doesn't exist? The only way I know of to prove something doesn't exist is through observing it's absence...

Not scientifically as you can not prove a negative.

No it is a silly idea and a dishonest rhetorical trick to ask for proof of non existence.
All that can be done is to demonstrate why we know something DOES exist and then show the lack of the same criteria and evidence that make it probable other things such as a god for example DO NOT exist.
However since there are a literally infinite number of things that DON'T exist I am not going to waste my time on that which is not, when there is so much that is to take an interest in.

That depends what you mean by ‘doesn’t exist’. By the very nature of exploring its existence it exists as something to be a explored. Have a look at negative theology. I suspect you would find it fascinating.

First we look at the definition of this "thing". If it is self contradictory then, there is not even need to check for existence as per definition something self contradictory can't exist (for example parallel lines in euclidean space that have only one intersection point).
Here you can say " This thing does not exist"

Then if the definition has internal consistency we look if it is falsifiable.
For example; There is a a blue cow in that room.
You open the door and verify if the cow is there, if it is not, there is not then A blue cow that lives on that room does no exist.
But is not always that you have capacity to verify. For example, you can see only white Swans thus you say that black swans does not exist. But you can't look in all the world to check it, so it becomes an open question. Unless you develop a capacity to check the whole planet, you can never answer this question with 100% sure.
Here you can say: "As far as our capacity to measure goes, we say we haven't found any evidence of its existence"

Then we get to unfalsifiable definitions:
Here we are entering in the garage dragon type of affirmation.
This kind of definition says that something that can't be measured because it does not interact with reality, or interact in a way that is disguised perfectly in the randomness of world, in a way that is impossible to measure.
This kind of entity is impossible to prove inexistent, mostly because for practical purposes its existence or inexistence will generate the same results as far as we can measure.
Here you can say: "By definition is impossible to measure or find its existence because it does not interact with known reality and its existence is impossible to measure."

So yes, in some cases is possible, in other cases you can just say that it is irrelevant for objective reality.

BUT You can purpose an infinite number of unfalsifiable or technically difficult to verify concepts. Here we have the Occan Razor that says that we should invest on simpler to test hypothesis and let the more complex after, this way we can get a better approximation faster. So unverifiable concepts are useless when you are trying to know something.