Producing soap from sodium carbonate and oil
In nature fat is stored as triglycerides (TGs): Three fatty acid (FA) chains bound together by a glycerol backbone. Olive oil is mainly composed of TGs, though it also contains small amounts of free fatty acids (FFAs).

An example of Triglyceride (from Wikipedia)



Soap is commonly made via the reaction of triglycerides  with a strong base: usually Sodium Hydroxide ($\ce{NaOH}$) or Potassium Hydroxide ($\ce{KOH}$). Though $\ce{Na2CO3}$ is a base, it is too weak of a base to be efficiently used in the traditional production of soap: It may saponify triglycerides but only at a very slow rate, if at all. So you are unlikely to produce much soap by mixing $\ce{Na2CO3}$ (of any source) with oil.

Soap can however also be made by reacting a weaker base with free fatty acid (FFA) chains; that is, FAs that have already been broken away from the TGs. $\ce{Na2CO3}$will form salts with FFAs, and it will do so at a much faster rate than it would saponify TGs. It can thus be used to make soap that way instead (and will, for instance, react with the small amount of FFAs in your oil). 

You could try to find a way to separate the FFAs from the rest of the oil (though it would be a highly inefficient process as you'd be left with the dominant TG portion), you could in theory also separately break down TGs into FFAs prior to saponifying them (using enzymes for instance), or (highly recommended) you could go the traditional route of using a strong base which will efficiently and (relatively) rapidly saponify both TGs and FFAs in your oil.

Splitting triglycerides is the "hard work" from a chemical point of view.



Sources

https://en.wikipedia.org/wiki/Saponification
https://en.wikipedia.org/wiki/Triglyceride
https://en.wikipedia.org/wiki/Fatty_acid
https://en.wikipedia.org/wiki/Sodium_carbonate
https://www.soapmakingforum.com/threads/how-much-sodium-carbonate-to-use-for-soapmaking.60798/