I agree that it may be too early for much automation. But there is still a lot QA can bring to the project to help it be successful at this stage.
If it were me on the project, along with learning everything I could about the requirements, I would be looking at what the customer(s) really do & what their workflow is, what our competitors might offer and anything we've developed previously that might be of use (good or bad) on this project.
I would try to get invited to any/all meetings on design & development so I could understand not only the product requirements, but how the coders are developing & writing the product. Take note where there are heated discussions, confusion or areas of concern - those are areas you might need to give extra attention later.
Be curious & ask questions. Ask about tests you might run, or the labels for fields, or what the customer expects response time to be - ask about everything. This confirms everyone sees things the same way (easier to catch it now, than later). I've been amazed how many times a 'harmless' confirmation question has evolved into a full 20 minute conversation that fixed a major issue on paper instead of when it came to test.
I work in an agile shop - so I would begin to draft up some epics, and if possible some of the first stories. They may need flushed out later, but start getting the ideas down. And begin looking at your requirements - do you have a specific format required for test plans, regulatory documents you'll need to fill out with testing, etc. If you don't know what those are now would be a good time to gather that information.
If you see something new to you, now might be the time to give yourself a crash course in it. (I once did an introductory course on medical coding based on the project I was on... not needed, but very useful when we got further in.) While things are slow for QA is the time to squeeze that in.
Being your QA person is only half time on the project all this may not be possible, but even tackling a few of these things will be good for the overall project.