Gold, gold, gold

People hate isolated starts but I love them
It's so easy to make friends (then sell them luxes/horses/iron) as no one covets your lands. If you play your cards right, no one would ever want to attack you all game, and even if they do, you climb the top half of the tech tree anyway and get frigates/subs (warmongers go the bottom half usually).
It's easy to get by with having a minimal troops (2-3 archers for barbs and CS quests)
You can expand whenever you want, so that NC gets up pretty fast.
You won't need to make settlers until your cap can make them in ~4 turns as opposed to 10 turns at the beginning.
etc.

btw if on King/Emperor, you can win with one, maybe two cities, pretty easily so don't sweat it too much

I do early wars a lot (also CS) and I go bankrupt and am very hated. There shouldnt be so much hate for conquest and you should be able to field an army early without going bunkrupt.

To avoid this you need to have TR as early as possible and that should help. You shouldnt build units - just a few. Go AnimalH and make a TR than you need Sailing and Engineering for another 2TRs to have 3 total. With that you should be able to field a small army and still have positive income. Ofc you need someone to send the TRs to. That needs you to be friendly towards them.

So just my experience - I think ancient&classical warmongering is broken and should be fixed.

Yes and without TRs you are basically srewed. So yeah in that kind of position you have to live with the deficit.

Yes I think the balance might not be optimal.

It is rather silly how it works yeah, seems like the dev's tried to balance it for competetive play, which seems like a complete waste of time to me, that being said, it can be relatively easily overcome with the trade route system they're basically forcing you into, on higher difficulties this is less of an issue, as you'll be prioritizing them anyway for the gained science, but on lower, especially when you've just started playing BNW, it feels rather counterintuitive, I recall my first game on BNW, on prince, I didn't build a single trade route but still managed to win, so it's all pretty relative.

And before trade routes, or if you can't set them up (wars, or otherwise crucial production), I tend to just sell every single thing I can, horses, iron, lux, open borders, embassies, usually this evens everything out enough so that I can rushbuy my 2nd or 3rd settler and a library for NC if necessary.
Unless you plan to go out conquering in ancient/classical you won't need strategic resources anyway, best early desense is the archery path (CB, X-bow), and I find that even on deity one or two of those combined with walls and oligarchy holds off pretty much anything.