There's no "first answer position" - since answers are sorted first by vote and then randomly (rather than in order of posting).
Posting an answer 3 seconds before someone else will make virtually no difference to the way people vote (unless some people check the timestamps and only vote for the earlier answer, the effect of which I imagine would be minimal).
In other words - this isn't needed. Post the best answer you can - if you notice someone else has posted an answer which you have nothing to add to (via the "New answers posted" banner), then stop writing your answer. Otherwise - keep going - how would knowing 73 other people are trying make a difference?