The operative verb in Matt 24L34 is γίνομαι (ginomai). In this verse the for is γένηται which is aorist subjunctive middle voice. Thus, it must be literally translated, "shall have happened" or similar. (English does not have an exact form of this part of the Greek verb.)
The verb γίνομαι (ginomai), meaning "I come into being, am born, become, come about, happen." (Strongs) is used in several ways such as (Thayer):
- to become, ie. to come into existence, begin to exit, receive being
- to become equivalent to to come to pass, happen, of events
- to arise, appear in history, come upon the stage: of men appearing in public
- to be made, done, finished
- to become, be made, "in passages where it is specified who or what a person or thing is or has been rendered, as respects quality, condition, place, rank, character" (Wahl, Clavis Apocr. V. T., p. 101)
Note that this verb does not ever mean anything like, "begin", "start", "initiate", etc. Thus, the answer to the OP's question is, "No". The verb cannot be translated, "to begin".