However I found a very early maturing variety of both
broccoli and cabbage. The broccoli is early dividend and takes 45 days to mature; cabbage is just a normal green variety, and it takes 40 days to mature.

So would I be able to direct sow them in early spring?

By 'early spring' I mean mid to late April, if weather cooperates; if this isn't feasible, then beginning of May.

The reason I ask this is because normally you transplant broccoli and cabbage out (after they've been hardened off) when they're 4-5 weeks old.

However if I started these varieties indoors then by the time they're ready to be transplanted, since they're so quick to mature, wouldn't they be ready to harvest if direct sown outdoors?

Another thing you can do is cover the planting area with black plastic to let the sun heat up the soil prior to planting your seeds. I'd say a month before you want to plant.