A month is not unusual, many companies (especially larger corporations) work on Net 30 or even Net 60 terms, meaning you should not expect payment for 30 or 60 days after delivery of goods/services. I would be surprised if there were no reference to these terms in your original contract, if they aren’t in there, then this is something that should be mutually discussed and agreed to in your initial negotiations.
You said you took this job to gain experience, and now you have also added some experience in the business end of things as well.
I would most likely remove the company and person’s name from your original post for now, while the terms of payment are being sorted out.