But I realized that I'm overlooking the crucial part, which is that you want to feel like she belongs to you. I think you're having trouble because you feel like she has "belonged" to a bunch of others.

Society definitely encourages that thinking, so I can see why you'd feel that way. But I think you will be much happier with her and others in the future if you try to eradicate this idea of your girlfriend being your property somehow. Then it will be easier to enjoy her as a companion who comes to you fully formed and independent, with everything that entails.