I do start broccoli seedlings indoors also, because they are a bit slow and I can give them a better start. Broccoli is extremely cold tolerant. I'm in probably a somewhat similar climate to you, and I plant broccoli seeds indoors sometime in mid-late Jan. Once it is a sturdy little plant in its own pot (say with at least two pair of true leaves), you could probably move it out to the garage. You would need to do that a bit gradually to harden them off, say taking them out for a few hours and then bringing them back in for the night and increasing the hours. Once they are fully hardened, they are frost tolerant. But in the garage, they will need lighting. It might be just as easy to just take them outside, starting in some sheltered spot and still bringing them in at night at first. I harden mine off outdoors and then plant them in the ground around mid-march, which for me is a month earlier than my average last frost date.
The tomatoes and especially the peppers are much more cold sensitive. I start pepper seeds indoors maybe in early-mid Feb, because they grow and mature slower. Tomato seeds I don't start until late Feb or 1 Mar. The tomatoes can go outside or in unheated garage when temps are 50 or above. Peppers need a little warmer than that. Everything needs some gradual hardening off. Late winter, early spring, I do a lot of bringing trays of seedlings in and out, depending on the weather and their degree of hardening.