I sometimes only leave 3 or 3 and a half hours between meals, but not as few as 2 or 2 and a half. I'd be a bit concerned about doing that, tbh, because of the amount of insulin still active in my system. I think it would be possible if you knew what you were doing in terms of calculating the carbs and the insulin, but if you're only recently diagnosed (sorry if you've had diabetes for ages, I'm going by when you joined the forum) it would be better to try to leave at least 3-4 hours between meals and ideally 4-5 hours, at least for now.
There's no reason you can't have a snack 2 or 2 and a half hours after breakfast, without any insulin, if you're hungry though, and then have your lunch and lunchtime insulin a bit later. If your blood sugar's lowish you could have a biscuit or something that's about 10g of carbs with no insulin, and if your blood sugar's higher you could have some cheese or nuts or something low in carbs like that.