What you are asking about is called tethering or tethered shooting. It's a fairly common use case in studio environments, like what you are doing with product photography.
Tethertools is a good starting resource to find out what tools, accessories, and software might be compatible with a particular camera; in your case, the Sony a6000 can be tethered, but tethered live view is not possible. That means that you can use a computer to capture an image, and possibly even control some exposure settings from the computer, but you will not be able to see the image on the computer while composing, before taking the shot. You will only be able to see images captured by the camera on the computer.
As far as tethering software is concerned, the following explicitly state that the Sony a6000 is supported (again, without live view capability):
- Capture One Pro — their support page states that Capture One Pro / Pro Sony is required for tethered shooting. Capture One Express does not support tethering. > $100.
- Sony Imaging Edge — apparently free for supported Sony cameras.
- Darktable — open source Lightroom "replacement" (in rough terms). It supports tethered shooting, and states compatibility with the a6000 (but again, don't expect live view shooting). Free.