Three weeks ago, I started my tomato plants from seeds. Usually they grow slow because the room I grow them in, is usually around 60 degrees. When it warms up outside so does this room and then I start my eggplant and pepper seeds.
This year I started them all at once. Instead of 60 degrees the room was around 80 degrees. My cucumber germinated in two days and all of the tomato plants were up in a week. The eggplants and peppers followed a week later.
My tomato plants are growing a bit too fast and are getting rather leggy so I re-potted them and buried the stem down in the dirt. Roots should grow from the buried stem.