I assume you are talking about starting vegetables from seed?
If so, you are early in my opinion. I lived on Long Island for quite some time and started tomato's, cherries and large fruit varieties, green pepper, cucumber, and egg plant from seeds. I grew them under and old shop light with a warm white and cool white tube in each fixture.
I would start the cuckes in early March. I would put them out first. Typically that was the last week in April.
I started the peppers, egg plant and tomato's in late March under lights. I kept the lights very close to the seedlings to keep them shorter and bushier. If you keep the lights too high, the seedlings tended to get very slender and tall.
I would put the peppers, egg plant and tomato's out in the garden around Mothers Day.
There is no need for a greenhouse in my mind.
I grew a second batch of cucumbers and started them right out in the garden. Usually around the first of July. I started pole beans in the garden around Mothers Day.
