I recommend that you purchase a springform pan. A springform pan has a clasp on the side, which, when released, enables the sides of the cake pan to "spring away" from the cake. There's no need to invert the cake to get it out of the pan.

If you need to bake this cheesecake now, without using a springform pan, I would use an 8” or 9” cake pan lined with parchment paper and also greased (buttered) to be able to remove the cake. It is very hard to substitute for a springform pan.