Russian: MANPADS usually don't destroy aircraft through raw force, usually they do so by hitting them with a 'shotgun blast' of shrapnel with the intent of disrupting enough systems that the aircraft fails. Double points if it compromises fuel tanks or engines and causes secondary explosions.
An SA-7 could take out a 747, for instance, if it hit an inboard engine, caused it to explode while compromising the inboard fuel tank, igniting the fireball, and then losing the affected wing. It'd be a lucky shot, but perfectly possible.
When MANPADS are succesfully used against civilian liners (and it will happen eventually), it will probably be two or three being used at once on a plane that has just taken off.
Regarding the LAX departures, it's over the ocean, yes, but a car stopped on Sandpiper or Vista Del Mar could unload a pair of shooters, they could fire their loads without any witnesses, and be driving before the plane hits the water.