Once she's out (if you're letting the bee's release her), she may start laying right away but it's not uncommon for her to take a while before she gets going. I typically check for eggs when I check to see if she's been released. Usually a few days. I'm terrible at seeing eggs so don't take my word for it but I usually see results in at least a week...maybe more. Others may have different thoughts.
I did my first inspection on Sun. one week after installation of the package. Queen was slow released. Found the queen in every hive. I saw honey and a little pollen but no eggs. Its been one week. All 10 hives have the same scenario. No eggs.
It depends on the condition of the queen in the package. If a queen goes off laying, it takes 10 days to get eggs flowing again. If she was caged the morning you pick up the package and you install that package by the next morning on already drawn comb, she'll be laying. If she's been caged 3 days, she may not be in laying condition any more.
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