Good advice, here. This is a tricky one. It definitely feels too early to be asking for this, but I also find the concept that work fits neatly into 40 hours to be ridiculous. We all know (at least in the kind of work I do) that it can expand to fill the time available--the work is never done. So whether I work 32 hours, or 40 hours, or 60 hours, there is always more work, so why can't we negotiate an amount of work with fair pay that is something other than the arbitrary 40?
I have successfully negotiated part-time work twice (as a professional, in a "career," and with direct reports both times). The first time, when I considered doing it, I asked around and was told not to, that my career would be over. But then I kept asking, and I found a woman who had done it for a year or two while her babies were little, and she was able to ramp her career back up, and get several promotions after coming back full time. So I negotiated 75% time, but only after I was comfortable with the risk that my career might never advance again in that organization.
I believe that as long as I stayed 75% time, I would not get promoted, but that I could have come back and resumed my career path had I wanted to. That said, I had worked for the organization for over a decade and had a strong reputation. And the people in that organization were/are very supportive in general.
After only 4 months in my current organization, I have asked to go 80% starting January 1. I shared my (personal/family) reasons for doing so and they have been very supportive, even said they want to do whatever they can to make it possible for me to continue to work there. Again, I had to be willing to take the risk that it might reflect poorly on me in their eyes, and am at a point in my career/life/set of personal circumstances where I'm willing to take that risk.
So...like many have said, wait until you know the place better, and they know you better, but then don't be afraid of going after what you want, as long as you can live with any potential downsides.