Double clutching makes engaging 1st while rolling a lot easier. Or, try blipping the throttle. Second gear never game me any problems, but I think on your roads you probably are best with third when you think you should be using second. Generally if I'm rolling at all, I'll use second. Idle speed in second is like 4 km/h anyway, so just go off the clutch, roll on the throttle after and it will pull away no problem. Has anyone tried launching from second? I wonder if that would actually improve the 0-60 times.
Do you have the Mazda 3 MPS? That's what we call the Mazda'speed' 3. I actually prefer the term MPS, because people keep incorrectly calling it the (southern american accent) Mahzda Three Speed! and that aggravates me to no end. If you do, then you have the same transmission as us.
Since second is also so short, I noticed that going around corners it was already doing 2000 revs or so, but only 1500 in third. This means that you'll also have to double-clutch downshifts to second when making turns, or use third, or blip the throttle before going down for a corner. If you're doing 30k or more, just use third anyhow.
My old car revved lower around turns and only had a 5 gears, so second was in it's sweet spot for engagement. This transmission revs a little higher so I've had to get used to double clutching before a turn. I personally find the drive-by-wire throttle system completely unfathomable for rev matching. It takes like a full second before the engine does what my foot tells it to (throttle tip in lag?). Yeah I'm being picky.