Can we train the model to detect real users with only positive labels? We have hundreds of thousands of customers records, and we need to take the benefits of our data to train a model that will recognize fake entries or unrealistic ones for our platform, where customers are asked to enter their names, phone number and zip code.

So, our attributes are name, phone number, zip code and IP address to train the model with. We have only data associated with real users. Can we train a model provided with only positive labels (as we do not have a negative dataset to train the model with)?
The problem which you have is a classification problem. You assume a class "good users" and a distinct class "bad users". You want to train an AI to tell the two apart, but all your examples are "good users". Any reasonable AI will draw the logical conclusion from those examples: all users are good users. That's a 100% match for the training data.