What component should I start when soldering multiple components?
Since there's BGA and QFN in there, you're not soldering these components one after the other, but you'll have to solder these all at once, using a reflow oven or at least a hot air gun, after applying solder paste to the pads.

When there's BGA involved, you'd very much want to apply that paste using a stencil.

The pin headers are special, because they are the only through-hole components: Reflow-solder the rest of the board without them, then solder them in manually (i.e. with a soldering iron). Unless you're really new to soldering, there's no chance you'd damage anything nearby when soldering these – pin headers must be the easiest thing to solder on this planet.



further comments:


if your memory is BGA already and you're space-constrained: you'd probably want to use a QFN or BGA package for your microcontroller, too.  I promise that after layout, you'll realize how humongous the pin headers are compared to the actual components of your circuit.
If you're doing this board design for hand-assembly, do yourself favors like putting resistors aligned to each other: makes SMD component placing with tweezers easier, and also heating up with a gun uniformly.
Don't try to overdo it with the "smallness" of the board. At well-known manufacturers in China, a 5×10 cm board isn't more expensive than 5×6 cm, so saving space in a prototype doesn't pay at all.
Also, realize you'll build a prototype. Nobody in this world had a perfect board after they designed a complex board for the first time. That prototype can be larger than what you want to deploy in the end!
Add plenty of test points where you can probe with a multimeter – it's darn hard to figure out what goes wrong if you're not sure whether all parts are powered, for example. Not having test points was my main mistake in my first designs.
Honestly, the way you've been asking this doesn't sound like you should be designing a board where you expect components to be packed that tightly. Start easier!


Also, if you were really planning on doing 0402 components with a soldering iron: my respect, I wouldn't have the nerve for that. In the sense that I would really have to quit the caffeine a day before I tried to do that.