Does Judaism believe in private property?
There are a few ways in which people can answer this question. In light of this, let me give you a few perspectives that will help.
First, we need to realize that Judaism is not monolithic. It might be better to speak of Judaisms (note the plural). So, there will be differences of opinions.
Second, there is a concept in Judaism with regards to private property. We know this, because there are commandments in the Hebrew Bible that speak of stealing. Think of command seventh commandment in the Decalogue (Thou shall not steal). In other words, you cannot steal, unless there is the concept of private property. The same can be said of the idea of coveting. You should not covet a neighbor's goods, because it is not your own.
Third, there is also a strand in the Hebrew Bible that speaks of generosity, charity, and compassion. So, even if private property is fine, one must use private property to help others. The reason for this is, because God is the chief inheritance from the point of view of the theology of the Hebrew Bible.
I should have added one more point. In Genesis 12:1-3, there is a pattern that emerges. Abram is blessed and he is blessed to be a blessing. So, even with the idea of private property, this private property is to be use to bless others.