Depending on jurisdiction, and the age of the person who disappeared, often times a parent or friend is told to wait a day or two.
An apparent TV trope that has become a myth on it's own, one is often told to wait to build tension in the episode/story.
The reasoning behind this may be because often enough the person simply ran away (or just ignores social medias and didn’t say anything), went out and got drunk, maybe hooked up and didn’t come home for the weekend. We the viewer of course know better!
On top of that, teenager or older who didn’t come home on a Friday night isn’t particularly suspicious...A Saturday night with still no phone call...is maybe strange depending on the person but not completely surprising and in tiny towns I could see the police station being closed on Sunday or close early, so a parent who maybe waited patiently all weekend for their child to call or come home would be finally suspicious enough to maybe talk to the police.
If this is a working adult, them disappearing from work Friday night, and not showing up on Monday for work without a call would be the only tipoff something might be wrong.
Friday is the ideal time to kidnap a working teenager or adult in the context of the show as its normal a person would be gone or difficult to contact over the weekend.
However if this was a child who disappeared on a Friday night, it would be much more suspect and illicit a fast missing persons response, I would assume.