Finding the queen, and when not to bother
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You almost never need to see the queen. You need to know she is there and laying, and eggs tell you that faster than she does.
Most of the time you do not need her
Eggs are the proof. A frame with eggs standing upright in the bottom of cells means a laying queen was present within about three days, which answers the question you actually had. Hunting for her after that is curiosity, and curiosity costs you twenty minutes with the hive open and the brood nest cooling.
New beekeepers hunt because finding her feels like competence. It is a useful skill and a bad default. The keepers who look fastest are usually the ones who look least often.
What to look for
Not the color. She is longer than the workers, with a tapered abdomen that extends past her wings, and she moves differently: deliberate, while the workers around her move in bursts. That motion difference is what catches an experienced eye, and it works in peripheral vision better than in a focused stare.
She is usually on a frame of open brood in the middle of the nest, because that is where she has been working. Start there rather than at the outside frames.
How to search without losing her
Little smoke. Heavy smoke sends her running and can drive her down into a lower box or, occasionally, out. Work calmly and in order, and check the frame faces as you lift rather than after, because she moves around the comb away from light.
Lean the first frame you remove against the hive outside, so you have room to separate the rest without rolling bees. Look at the frame you have just lifted and the two faces now exposed in the box. If you have gone through the whole box without her, close it and move on rather than starting again; a second pass of a now-agitated colony rarely succeeds.
Marking her saves this time later and is the one good argument for finding her when you do not need to.
When you genuinely must find her
Requeening, splitting a colony where she must end up on a known side, and confirming a suspected failure when there is no brood at all to read. Those are real reasons.
If you cannot find her and you need to, the usual answer is not to look harder. Shake the bees from the brood frames through a queen excluder into an empty box, or split the colony and check both halves for eggs in a few days. Both are less elegant and far more reliable than a fourth pass through the same boxes.