would there be any algorithm that could be used to calculate approximately how much btc could be mined for about 9 months?
Let's see:
+-------+------------+------------------------------+
| block | unixtime | timestamp |
+-------+------------+------------------------------+
| 0 | 1231006505 | Sat Jan 03 18:15:05 2009 UTC |
| 1 | 1231469665 | Fri Jan 09 02:54:25 2009 UTC |
| 22000 | 1251826171 | Tue Sep 01 17:29:31 2009 UTC |
+-------+------------+------------------------------+
The whole network mined around 22,000 blocks in 9 months. That means something like 1,100,000 BTC for all miners combined.
Google ai told me it would be 550000 to 650000 btcs, would this somewhat exaggerated?
That would mean a miner with 50% or 60% of the network's hashrate. For a small miner, for example with 10% hashrate, it would be something around 100,000 BTC instead.
Any quantum equation or quantum leap that would allow us to calculate approximately how much btc would be mined?
Why do you need anything like that? You can see network timestamps, because they are public. You can calculate all coins in circulation, by multiplying the number of blocks by 50. And then, it is just a matter of splitting it between network participants. So, how much hashrate your node would have? 10%? 5%? 1%? Or maybe 50% or 60%?
Also, if you have the hardware you want to test, then you can just run some custom signet, let the difficulty adjust, and compare it with the original one. Initial signet difficulty is easier, than mainnet in 2009, so it should be easy to measure. And even if not that, then you can still measure timestamps between blocks.