Any way it's possible to try this without am ice-cream maker?

I think you can. It does require more manual work on your part. You can make the ice cream base, freeze for 1-2 hours, then break up the slightly frozen base with a beater or food processor. You would have to do this a few times as the mixture freezes. This mimics the churning process so that you have a smooth frozen product as opposed to one frozen block of ice. I think you can also do this by putting the base into a Ziploc freezer bag and squishing the semi frozen mixture into your hands to simulate churning.