Colour balance is an issue with all cameras and has been since colour film was used and analog television days. Changing the colour space might help, but that is not it's purpose. The purpose of the colour space is to best utilize colour response to the two main outputs: sRGB is designed for use with colour monitors (computer screens and such) which in turn were related to early TV technology, and AdobeRGB was intended for prints. AdobeRGB utilizes colours outside the expected response of colour monitors. The simplest rule is that if you are going to make prints then use AdobeRGB, and for all else use sRGB.
But "colour spaces" refer to outputted picture files, not "raw" data files. It has no effect at all on "raw" files. Most of us on this forum probably use "raw only" or "raw + jpeg" output. I doubt if many of us use "jpeg only". I use "raw + jpeg" and "sRGB" on my Sony a5000. If the JPEG comes out with a good appearance I am very happy. If not, then I just ignore it and make my own output based on the "raw". If the JPEG is very close to what I want, then I might make a small correction to the JPEG instead of starting with the "raw".
But what you could do is start learning to control the "Color Balance" in the camera. As far as I know, the "Color Balance" control does not affect the "raw" files. It is applied to the JPEG. To make a difference on the "raw" file, real optical filters are necessary. Your a6000 should have an array of pre-set colour balances, and also a "full" adjustment base on colour temperature ("K"). But that is probably a helpful but incomplete control. A proper adjustment needs at least "Color Balance" and "Tint". Traditional "Color Balance" only adjusts between Blue and Red. "Tint" is the "Green" content. And then all this is affected by "saturation" (aka "intensity"), brightness and contrast.
But the main thing about using controls like these in a Mirrorless camera is that you should get a good idea of what result you will have when looking at the viewing screen. Personally, I don't really pay attention to colour balance in the view finder for still pictures, because, as I wrote above, if I don't like it, I just change it later in editing.
But if you manually adjust the colour based on the display, you should be able to come close, and may even get it perfect.