Simple: if it's important to you to volunteer, then you make the time. Volunteering doesn't have to be for 20+ hours per week, and it doesn't have to require a lot of effort to do. Pick something you're interested in, or that matters to you, and figure out a way to use it to help people. So, if you're writing software anyway, then help clueless people like me set up their webpages. (No, I swear I have no vested interest in this suggestion!) Or, help run a computer class at your local library or senior center. Or, pick X hobby that you like doing anyway, and help other people learn to do it.
I was a chemist before going to medical school. My premed volunteering included being on staff for SDN (which dovetailed nicely with the fact that I spent too much time surfing this site pretty much every day anyway); doing science demos for elementary school kids (really, who doesn't like ice cream made using liquid nitrogen no matter what their age???); and mentoring undergrad student workers in the lab (I was there working anyway, and they could actually help me with my projects if they learned what to do and stuck around long enough!).
I also volunteered at a hospital for a year, which did require more effort, and I did that by spending two hours from 6-8AM one day per week before I went to the lab. Losing two hours of sleep was painful sometimes, but so is losing sleep during your medical training sometimes. Think of it as early conditioning, if you like. 😉