Balance and meta, can they exist simultaneously?

It depends on your definition of balance.

Having everything truly 100% balanced would basically require homogenizing everything to the point where everything is the same, which doesn't make for terribly interesting gameplay in a lot of cases. There are however a few things you can do to create a sort of "balanced set of imbalances".

If we look at a game like Counter-Strike, most of the pistols aren't as good as the assault rifles. They are however, cheaper in a game where the amount of money you have is important to keep track of. Buying a weaker but cheaper weapon as an "economy round" is a very common tactic in that game. It's not balanced in the sense that the Five Seven is just as good as the M4A1, but it is balanced in the sense that they both have their respective roles in the meta.

Map can also play a role. If we got a map that has a lot more tight corners and small rooms, then weapons with poor accuracy and good damage output will naturally do better than something like a sniper rifle. The reverse is also true of more open maps with larger areas to traverse.

I don't think you can have balance and meta if your idea of balance is that everything ought to be equally as good in most situations, but you can have it if your idea is that some things are balanced to be better with some other factor(cost, skill, ease of getting the weapon/skill, etc.) off-setting its power.