Did you install a pilot bearing or a pilot bushing in the crank? Sometimes a pilot bushing is sticky and makes it hard to shift into first from a stand still, particularly if you didn't align the bell housing when you installed it.

You may also have an off-center pressure plate. I've seen more than one pressure plate that needed adjustment of its face before being installed for the fist time. The symptoms are what you describe.

Don't drive it with no play. As everything heats up, that lack of free play will turn into pressure on the T/O bearing which will result in slippage and a wasted clutch disc.