Earliest you can enter US to apply for TN?

I know some prior threads have touched on this, but I wanted a more definitive consensus.
E.g., my job starts on late Aug. Can I enter the US via pearson airport to apply for the TN 3 weeks before or 4 weeks before? Or is 2 weeks or less the safest route? Should I ask my employer to just not list a start date or can the start date be really vague like sometime in "august"?

The best practice is to have no start date on the letter. the letter itself should be dated.