When do I start dosing fertilizer into a newly setup planted tank?

The short answer is that you should start dosing water column fertilizers as soon as you have plants in the new tank and no later.

But why? Don't my aquasoil leech nutrients for the first few weeks?

Some folks think that because they have a rich aqua soil tank, that they can skip dosing fertilizers for awhile as the new soil will leech out nutrients at the start. A lot of aquasoils are spiked with ammonia which serves as a nitrogen source long term to feed rooted plants. However, most aquasoils don't leech all required nutrients at a sufficient rate. Many aquasoils may leech ammonia/nitrates, but may lack sufficient potassium/magnesium. If you do not dose from the start, you are taking a bet that your tap water has small quantities of the nutrients required for the newly planted tanks to get through the adaptation phrase. Plants requires a full set of nutrients to grow optimally; having an excess of N because of ammonia from soil, but lacking potassium or magnesium is not helpful.

Water column feeding of non-rooted plants

New plants have no established root system, which limits their ability to draw nutrients from the soil. However, aquatic plants can draw nutrients through their leaves as well; therefore having nutrients in the water column gives them easy access to nutrients before their root zone is developed. When plants adapt to a new environment, easing transition stress is important. Giving them plenty of CO2 and adequate nutrients is an important step in preventing melting and accelerating adaptation to the new environment.