The time to receive the fee payment receipt (and the case number) is the same, irregardless of whether the LPR parent petitioned for their child, spouse or whatever: anything between 10 to 14 days from actual receipt date at USCIS.
Relax. The waiting time for a green card is 2+ years.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.