That number is child's play compared to numbers like Graham's number. The exponent of Graham's number is so large that it can't be written down. 30 is pretty easy to write down. For comparison there are about 10^80 atoms in the universe. That's still a tiny number compared to Graham's number.
Graham’s Number is impossible to write out using a powers of literal numbers, so it’s still not even close.
There are 10 billion people * 100 uC chips / person * 10 years of life / uC chip * 10^13 microseconds / year * 1 clock cycle / microsecond = ~10^26 clock cycles
If you wanted a time-series that shows how this number evolves over time, you would end up with a very interesting history of tech book. Something like Milton Friedman's "A Monetary History of the United States."
I would buy it / crowd fund it.
If all you really want to know is "number of cycles" you should probably research oscillator manufacturers.
If you're actually interested in the "volume of compute" you should start with 10K's for Intel and Xilinx, and fan out to their competitors. Use market capitalization over time as a filter for inclusion in your tally, as you can't research every manufacturer.
Rayo’s number is actually a function R(n) where n=googol. You can define much bigger numbers just by using a bigger n, e.g. googolplex. For something even bigger still, you can iterate the function. Think about Rayo’s function iterated Rayo’s number times.
You could make a rough model based on educated guesses and perhaps not even be that far off the actual number.