Just by following references in the Wikipedia about the carbon cycle I found this book chapter https://scihub.wikicn.top/https://doi.org/10.1016%2FS0070-45... that contains numbers (and error bars), alas from 1985. I'm confident that our knowledge about the carbon cycle has improved since then, given the amount of research climate change has gotten in the last thirty years.
Yes it's from 1985 and no it doesn't actually give a number either.
The fact that you can't find it and have to go to 1 article which isn't even giving you that number, should tell you that maybe you haven't gotten all the facts here.
This is exactly what started my journey from worrying about the climate to understanding it to realizing the base for all this is much much much fragile and much much much more politisized.
I spent about 20 minutes looking for that reference. I'm sure an actual climate scientist could provide you with a better reference.
Page 450 has a table. Historic CO2 concentration: 280ppm, "current" concentration 341ppm: a 21% increase. From that and the 60 * 10^15 moles C in the atmosphere in 1982 we can deduce around 50 * 10^15 moles C in 1800 in the atmosphere. That seems to be in the right ballpark of 14 * 10^15 moles of emissions from fossil fuels: not all of the carbon ends up in the atmosphere, e.g. some is dissolved in the ocean. Certainly the difference is not large enough (and doesn't have the right sign!) to support the theory that man made carbon dioxide didn't contribute the majority of the extra carbon in the atmosphere.
