No. It helps, but it isn't necessary.
(Disclaimer: commentary below refers to ancient era starts, and may not be applicable in other settings).
Why is it not necessary? Because the fundamental problems that need to be addressed in the early going are the same (how can I raise the happy cap? how do I expand my borders? how do I defend myself?).
It helps, in that the goal gives you something you can use to judge the choices that the game presents to you.
However, its a very distant target to aim for, especially when you don't have very much information about the map. Much easier to find a reasonable objective at a comfortable distance, and figure out how to work toward that.
I tend to think that, at normal speed, 1000 BC is about where your first goal should be. In other words, you should have some sense for what your civ is doing that far ahead. The information you have at the start will be the main basis for choosing this goal.
As you gather more information, you may find that you ditch that goal for another. My gut says that by 3000 BC you should be pretty confident what things are going to look like in 1000 BC.
As a rule, people here love picking at other people starts (see any ALC: six pages of discussion over where the scout should move prior to setting the first city). So what I would recommend is that you post a sample start, and invite comments.
Here are the elements that I would include:
1) screenshot of the initial starting position, with the grid and the resource markers turned on.
2) a description of your play up to 3000 BC or so (especially justification for your choices)
3) the goal you chose for 1000BC (ish)
4) and outline of your play to that point
5) description of the situation at that point, and where you think you should go next.
One further suggestion: concentrate on the broad strategic strokes, rather than the tactical details.
I more or less agree with VoU except that I stick with the safe, tried and true strats:
1. If you're isolated, think Space Race vic. Maybe cultural if you are set up properly for it and have enough cities (nine).
2. If not, go for domination. If you get out of control early you can go Conquest, if you fail domination you'll probably have enough land and hence production to win a space race, etc. Domination is a great default goal to have and the one I always go for if not isolated. Having enough land and pop also means having control of the UN if you care for Dip Vics (I don't; I think it's boring as hell).
3. You need at least a few trading partners/non-enemies so try to war selectively. I used to try to befriend one flank and then mercilessly pound the other to extinction. These days I actually try to befriend anyone really far away, while exterminating my immediate neighbors. See what works for you.
4. If you're still building up, give tribute to anyone who has the military to back up his/her threats. I love giving away crappy amounts of gold and/or tech for the 10 turns of guaranteed peace and +1 diplo.
5. Make advantageous tech trades and resource trades. I love trading away spare strategic stuff like copper, since later on the civ won't care for it but will still be stuck with the copper bill. Heck I trade away my last bit of copper if I don't need it for Cathedrals or Statue of Liberty.
6. Don't expand too rapidly or you will fall behind in the tech race. Depending on your UB, traits, and if you have CoL (I love the Oracle->CoL slingshot), you should keep it down to about 4-6 starting cities. Try 4 and using them to make barracks and to build and whip axemen early on to weaken or annihilate a neighbor. Then whip courthouses in all your cities, including the new ones.
7. I spend all game at 0% espionage. Great Wall's settled super spy does fine all by himself. Later courthouses, jails, etc. help even more. That spare commerce goes to science of course.