You don't need phosphorus unless you have a soil test indicating a need for some. Starter fertilizer has a lot of phosphorus so that the seed will be in direct contact to phosphorus. Once the roots start developing, they can get their phosphorus from the soil, assuming the soil has an adequate supply. Synthetic phosphorus inhibits mycorrrhizae, so it's best to use it only when the soil is lacking it. Excess phosphorus has detrimental environmental effects too.

Perfect, thanks! I did know somewhat of the environmental issues but wasn't sure if the new lawn would need it or not. So for a late fall, pre-NH-winter feed what would be a good blend/amount for the young grass?

If you're doing it in early to mid October, a slow release mostly nitrogen fertilizer, which probably has some potassium too, would be good. For the late fall feeding, which is done after the grass stops growing but before the ground freezes, use a fast release nitrogen. You can do both. Most fertilizer for cool season grass should be done in the fall.

Pertect, thanks so much!