I haven't played as Brazil yet, but I'm a big fan of the Aztecs and when I play them, I tend to encounter a ton of jungle in most starts. From that, here's my advice:
1) Get a religion simply to get Religious Community (up to +15% production, 1% per believer). This goes a long ways toward making your few decent production tiles per city really count.
2) Use trade-routes to move production around after you get workshops up. All it takes to get a city in dense jungle off-the-ground is building a workshop and one other production booster (stables for horses, forge for iron, etc.). With trade-routes, if you can dump in so much as an extra +8 production on the city, you can get these up far quicker than usual without having to buy them with gold.
3) Bee-line Bronze Working and steal workers from nearby CSes, then cut some of the jungle. Not ideal, but better than option 4 directly below.
4) Without CSes nearby to steal workers from, or if you don't want to anger CSes in general (as Aztecs, not a biggie, but Brazil is in a position to rely on at least cultural CSes), an absolute last-resort can always be to go Liberty, get the free worker ASAP, bee-line bronze working, and cut some of the jungle that way. Depending on difficulty level, you could even try getting the Pyramids wonder as well.
Now, as to the comment about civs without early uniques:
* Brazil can always get a Writer's Guild up and use Liberty, or even the happiness from staying very small (just capital and one other city, usually) with Tradition to get an early carnival and try getting the boost for at least Great Writers. If you delay using the Liberty free Golden Age for a little bit, you can throw in some of the other guilds. Thus, I wouldn't say there's absolutely no use for uniques in the early-game as Brazil, but I agree that they are a late-bloomer, for sure.
* To tech quickly, stay small (BNW adds 5% penalty to science per city) and focus on getting good food yield, libraries, and the National College up, all as top priorities. You obviously may need to build a handful of units, depending on circumstances, but try to get most of the units through completing quests to ally a militaristic CS to save production. If lucky, you may have enough gold to buy shrines and get a pantheon up to get a faith-yield going and found a religion, which will let you choose Religious Community as I suggest before. All of this better helps to set-up to build/buy universities quickly, too, which will help tech to Acoustics faster after you tech the lower half to get Brazilwood camps.
* Without any early uniques, you're free to be somewhat creative with what you do, and you sometimes have to be creative.
* Because your uniques come into play much later, you can be slightly less worried than usual about how far behind you are. The Pracinhas comes into the game quite late, yet will help keep Carnivals going at a time when you are really hoping to polish off the cultural victory.
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That's all I've got. I've not played as Brazil yet, so some of this is conjecture, but
a) in terms of dense jungle starts, I have a lot of experience as the Aztecs, and
b) in terms of early-games devoid of uniques, I've played the Ottomans (only the UA is even remotely helpful early on) enough to know what it's like.
Hope some of this helps!