How long do I have to wait to have an immediate dental partial out the day after you received it?

Dr. discretiion. It usually depends on the number of teeth involved. If there is a large number of teeth removed i usually have the patients wear for 24 hours and have them return the following day for a post op visit and check of the partial. I will usually remove the partial for them first, adjust if necessary, then instruct them on how to remove/replace it and care for it.
Be patient. If your dentist instructed you on how to put the partial denture in your mouth and how to remove it, then it would be ok to remove it only a few hours after it was delivered to you, if you're having discomfort. If you're unsure about removing it and putting it back on, then i'd suggest to wait until the next day and just drop by for a few minutes at your dentist's office, so they can evaluate.