Is there any specific meaning if i put "comma" before "with" ?

I agree with you that the meaning doesn't change any. The comma is a matter of "style" (aka punctuation). This could stand alone, as it's own sentence: "The child cried loudly." The rest is elaboration on the circumstances, and is not necessary to convey the basic idea of the sentence. In that sense, I guess it is a "subordinate clause" or something like that---A grammar book would tell you, but I'm not looking at one of those.

The comma, as used here, is designed to indicate a slight pause in the way it would be related if spoken. It may also be deemed to be "required" to offset what I'm calling the "subordinate clause," technically speaking, but I'm not sure about that. I never memorized grammatical terminology (and I never will).

Using the comma is optional, but it does change the implied meaning of the sentence. Using the comma tells the reader that the content of the prepositional phrase (in this case) is non-essential information. Leaving out the comma implies that it is essential. https://owl.english.purdue.edu/owl/owlprint/607/

I'm sure you're correct, in theory, FBM, but in a case like this what information is "essential" and what isn't would seem to be highly subjective. In other circumstances, there may be an objective difference, but I can't see it here. Put another way, what a comma "tells" someone else may be nothing of substance.

And if you intend a different meaning by using the comma, then it is not really "optional" for the purpose of conveying your intended meaning, is it?