If your main character is always late, that fault may in fact prove to an important factor in solving the case. If you can let agents know that 86 million people I made that number up are soap carving fanatics, then you might have an original new hook for a cozy series.
Community at large Your series, especially if it has legs goes beyond the first three books will eventually grow to include dozens, if not hundreds of characters.
Cozies have evolved.
Alternately, she can have a network of friends who might overhear or observe the actions of any of the above professionals, and pass them along. As soon as I wrote that I thought of Sherlock. Sheila Connolly, TheNew York Times bestselling author of three cozy series including The Orchard Mysteries, says that while Christie and Dorothy Sayers inspired her and most of her colleagues to write in the genre, the pacing of cozies has changed over the years.
It could be that the sleuth is part of a small English village. The precipitating crime either occurs before the story starts or soon after it begins. These people include the suspects of whom the criminal is actually oneinnocent bystanders, and those who may help the main character.
Again, this is something I use as a tool to more quickly jump into my book.