Didn't get an email from Target immediately following application submission. What should I do?

Don't worry about it. Target is like that. They will get in touch with you if something goes wrong. To old belif and a few years ago a mention that Target was attacked and hacked. Into their systems so not only their applications but also their consumers had trouble with their credit card information being taken. It's either that or their system is slow. They will get in touch with you if they find your application and something went wrong. It's not you tit's them. Also if they schedule you and reschedule your time be ready to either make it their early or not take the interview at all. If you have an appointment somewhere else that same day go to their appointment or decide which one is most important. Through I will never trust a Target or want to work for one. They are slightly two faced. But it's usually the people not the company itself.

move on they aren't interested in you, if they were you would have received an email