Do I have to spend all of my skill points before starting the game?

At the start of Deus Ex, when you begin a new game, it asks you to select some base character abilities and gives you 5000 skill points to spend;

Do I have to spend all of my skill points before starting the game?

No, you do not have to use up all of your skill points during character creation, in fact you don't have to spend any of them at all. Any skill points that you don't spend will still be available to spend and won't be lost:

These can then be spent once you're in the game as the need arises, however keep in mind that without any weapons skills your weapons will be very difficult to aim and do less damage than a trained weapon skill.