Time from emergence is fairly irrelevant. It could be six weeks before she gets mated and starts to lay. A few days is the normal expectation 3, 4, or 5 after mating - does it really matter?
I might wonder why it is important to you? The usual recommendation is to leave the colony alone for three weeks, after expected emergence date, before checking for brood. No point in interfering earlier as that is more likely to cause disruption, and you need to check brood pattern and that it is not drone brood, so some cells need to be capped. That, of course, means in decent mating weather conditions.