I assume you are referring to store bought pasta. If you purchase Angel Hair, Vermicelli, and other very thin pasta, in the time it would take you to heat up a sauce, the pasta would be cooked. Just put a cover on the pot when you are bringing the water to a boil. It will heat up faster.
Are you planning on feeding a three month old infant pasta with tomato sauce? Why not start with cooking small helpings of veggies and other foods. Take a look at the baby food section in your grocery store for ideas of different foods you can make ahead and freeze. At her age, tomato is acidic and could be upsetting to the baby's stomach and digestion system. If you are going to feed her pasta, toss it with butter instead.
Illegitimi non carborundum!
I don't want my last words to be, "I wish I had spent more time doing housework"