How soon should you reject someone
There are no 'shoulds'. Get rid of the idea that there are 'shoulds'. We have laws, and apart from that, there are NO guidelines, there is NO advice, there is NOTHING anybody here can tell you about what's ok and what's ok. It might sound a bit like 'Oh, shit, how the hell am I supposed to know what to do, then??', but the fact is this:
YOU know the answers, and YOU are responsible for making the right decisions, for YOU. This is ALL ABOUT YOU.
It's perfectly ok not to respond to a message for a week. Some people will find that ok, some will not. What are YOUR feelings about it? It's perfectly ok to want a response within 2 days. Some people will find that ok, some will not. What are YOUR feelings about it?
Make your decisions on what your feelings are, rather than what you think should be happening. So if the other person doesn't respond for 3 days and it makes you think 'Um... feels a bit like he's not interested in me much...', then deem that persons natural responses, from the off, to be something that makes you feel he's not interested in you much. Then work out if that's how you want to feel in your relationship.
Go on dates if the person has you thinking 'I like the timing of your responses; they're not too quick for me, and not too slow for me, and I like the things you say; you seem respectful of me and you listen and respond in a way that I enjoy'
If anybody has you questioning yourself ('He seems to be taking ages to respond but am I just being oversensitive? Am I getting it wrong? What should I want?') then back away. You simply won't question yourself in a healthy relationship. Think about your closest, nearest and dearest friends/family. Think about your relationships in the past, when they've been healthy and happy. Questioning yourself and questioning their whys and wherefores simply doesn't happen.
Take responsibility for yourself: what your future partner will do at the dating stage (and mostly at all stages) are things that make you feel nice.