Hey Maria,
Normally I would recommend the use of a counter output since you can actually specify an initial delay. For those of you reading this who may be intereted, you would use a start trigger on the counter task and then reference the counter as your sample clock source for the acquisition task. The counter output would not start until the initial delay had passed, which would be clocked from the moment the trigger occurs. Using DAQmx, you can actually specify Cnt0InternalOutput as the source for the AI sample clock.
Maria, I'm afraid that your card does not support counter triggering because it is an older E series board. In your case I believe your best option will be to disregard the samples you don't want. It won't be any less effective than the method I described above, you'll just have unwanted samples moving across your system bus, but the result should be about the same.
Let me know if you have any further questions.
Elijah Kerry
NI Director, Software Community