The first premise of the Kalam Cosmological Argument for the existence of God The first premise of the KCA is stated as:

Premise 1: Anything that begins to exist must have a cause.

The contrapositive statement for this should read. If something is not caused to exist then that something does not have a beginning. 

My question is related to the trinity. Would it also be true that anything that has a cause must have a beginning? If applied to the second person of the trinity should it not follow that since the Son depends on the father for his existence. ie. The second person of the trinity is the only begotten Son of the Father, then the preexistent Son of God must have had a beginning?

Please help.
It sounds like you think generation of the Son by the Father implies there was a time when the Son did not exist; however, all three Persons are co-eternal.

St. Thomas, in Summa Theologica I q. 27 a. 2 ("Whether any procession in God can be called generation?") c., distinguishes between and compares the two senses of "generation":


  The procession of the Word in God is called generation. In proof whereof we must observe that generation has a twofold meaning: one common to everything subject to generation and corruption; in which sense generation is nothing but change from non-existence to existence. In another sense it is proper and belongs to living things; in which sense it signifies the origin of a living being from a conjoined living principle; and this is properly called birth. Not everything of that kind, however, is called begotten; but, strictly speaking, only what proceeds by way of similitude. Hence a hair has not the aspect of generation and sonship, but only that has which proceeds by way of a similitude. Nor will any likeness suffice; for a worm which is generated from animals has not the aspect of generation and sonship, although it has a generic similitude; for this kind of generation requires that there should be a procession by way of similitude in the same specific nature; as a man proceeds from a man, and a horse from a horse. So in living things, which proceed from potential to actual life, such as men and animals, generation includes both these kinds of generation. But if there is a being whose life does not proceed from potentiality to act, procession (if found in such a being) excludes entirely the first kind of generation; whereas it may have that kind of generation which belongs to living things. So in this manner the procession of the Word in God is generation; for He proceeds by way of intelligible action, which is a vital operation:—from a conjoined principle (as above described):—by way of similitude, inasmuch as the concept of the intellect is a likeness of the object conceived:—and exists in the same nature, because in God the act of understanding and His existence are the same, as shown above (q. 14 a. 4). Hence the procession of the Word in God is called generation; and the Word Himself proceeding is called the Son.