OP, the situation you describe is called "assessing the risk". As you wait at the controlled intersection, you are trying to figure out if you have enough time to complete your manuver safely, before approaching vehicles threaten you. To give yourself confidence in completing these manuvers safely, you should time each manuver. If you are waiting at a stop sign at a 4way intersection there are three possible manuvers: Left turn, right turn, or straight ahead. Time yourself by counting; one thousand and one, one thousand and two, etc... from the start of your manuver until you complete the manuver. After you have done this, you now have an idea of how long it takes you to complete each manuver. For example; a left turn may take you 5 seconds to complete, right turn, 3 seconds, straight ahead, 4 seconds. Now, while you are waiting at the stop sign assessing the risk, start counting seconds on the approaching cars. Find a landmark on the side of the road; a sign, fire hydrant or something you can use as a point of reference as to how many seconds the approaching vehicles are from you. If the approaching vehicles are inside your safe threshold, wait until they pass; if they are outside of the threshold proceed expeditiously. IN ORDER TO DO THIS SAFELY YOU MUST ALSO BE ABLE TO ESTIMATE APPROACHING VEHICLES SPEED.
This gives you a plan of action when faced with the situation you described... Before long, you should become quicker and more accurate at "Assessing the Risk"
Hope this helps you! Remember; the bottom line is don't venture out into the path of another vehicle until you are sure you can make it safley!