For missing children there is the National Child Search Assistance Act of 1990:
National Child Search Assistance Act of 1990 - Requires each Federal,
State, and local law enforcement agency to report each case of a
missing child under age 18 to the National Crime Information Center
(NCIC) of the Department of Justice.
Requires States reporting
under this Act to: (1) ensure that no State law enforcement agency
establishes a policy which requires a waiting period before accepting
a missing child or unidentified person report; ...
[Source]
There is also Suzanne's Law:
"Suzanne's Law" amends Section 3701 (a) of the Crime Control Act of
1990 so that there is no waiting period before a law enforcement
agency initiates an investigation of a missing person under the age of
twenty one and reports the missing person to the NCIC of the Department of Justice.
This law was signed by President Bush as part of the national Amber Alert bill on April 30, 2003, requires police to initiate prompt investigation into missing young people.
[Source]
What about missing adults?
From the Arkansas Crime Information Center:
There is no waiting period before a person can be entered into the
NCIC Missing Person File.
Arkansas law requires all missing persons to
be entered immediately.
From the Wyoming Attorney General's Office:
NCIC does not require a waiting period for the entry of a person into
the NCIC Missing Person File.
Of course, just because a waiting period is not required doesn't necessarily mean that one can't be imposed. But I haven't yet found a state that does so.
Examples:
From the Washington State Attorney General's Office:
You may have seen on television or heard that you must wait 24 or even
72 hours to report someone missing. This is not true. There is no
required waiting period.
From the State of California Departement of Justice:
There is NO waiting period for reporting a person missing.
All
California police and sheriffs' departments must accept any report,
including a report by telephone, of a missing person, including
runaways, without delay and will give priority to the handling of the
report.
From The Texas Departement of Public Safety:
Under Texas law there is no waiting period before a record of a
missing person can be filed.
From the Departement of Maryland State Police:
§ 3-601. Procedure for taking missing person reports:
(a) Mandatory waiting period prohibited.
(1) A law enforcement agency may not establish a mandatory waiting period before taking a missing person report.
From The State of Connecticut:
It is an incorrect assumption that 24 hours, or any other time frame,
must pass before a law enforcement unit will accept a missing person
report.
There is NO waiting period for reporting a missing person.
From the Utah Departement of Public Safety:
THERE IS NO WAITING PERIOD TO REPORT A MISSING PERSON.
It is mandatory with many federal laws that the report be taken
immediatley and entered into NCIC within 2 hours for missing persons
under the age of 21. (Protect Act, Suzanne's Law, and the Crime
Control Act of 1990)
Summary:
For people under the age of 21 a waiting period is explicitly forbidden.
And in general, there doesn't seem to be a law that demands a waiting period. On the contrary, there is no waiting period for entry into the NCIC (and several states explicitly emphasize that there is no waiting period).