Depends on the kind of escape. Just putting a 'familiar' box/carrier at the spot of the escape would have worked the next day.
If you had kept the cat indoors for a week at its new home it can find its way 'home'. Check the previous home as well.
I had a cat disappear for a couple of months, believed it 'stowed away' in a friends vehicle (who lived in the next town). He came home (skinny) with his paws swollen three months later.
At least you have an idea that it was not 'taken' by a testing lab.
Also, check the animal shelter, and homes in the neighborhood of the escape.
Put up Wanted lost animal Posters in the area including the supermarkets and other stores.
I don't like your second paragraph, it implies if not saying outright, that you don't really want the cat back...