I don't think an open invasion is necessary, but the Yeerks could have been more aggressive, I figure. While you might be able to get people to get comfortable with brain slugs, why bother trying? It seems to me that first world countries are pretty ripe for infiltration on multiple fronts. The Sharing was a pretty silly front organization, and cults are small potatoes anyway. But look at homeopathy, acupuncture, and other "alternative medicine" practices. You can get lots and lots of people to subject themselves to rather weird procedures that involve them being alone with a stranger with just a bunch of hand-waving about quantum mechanics and chi.
Make the central pillar of your cure-all be some kind of "sensory deprivation" helmet, which also happens to have a compartment for a yeerk to hide in, and you've got a pretty effective front organization. The alternative medicine folks all tend to stick together, so you've got pretty easy access to a large and gullible group of people right from the start. Then you issue public challenges to skeptics in the medical community to try out your method for their migraines, cancer, etc. Of course, they emerge claiming that it's nothing (thus cementing your credibility in the alt-med community), but afterwards you've got a Controller doctor who can introduce yeerks to any patients that they put under anesthesia (or who just spends the night in a hospital, after a point). It's just a matter of time from that point on.
But, for my part, I wouldn't bother trying to take over the US or most of Europe. I think you could do it rather easily, perhaps using something like the approach outlined above, but you're still looking at years before you can openly operate on the planet, and procuring new, useful hosts is at least somewhat urgent. Fortunately, the yeerks don't care about human society or technical know-how, and a Controller from a third-world country is just as good as one from a first-world country. So, on the first day of your assault, you take down every satellite around the Earth and glass much of the US and Western Europe (and some of Russia, India, and China), along with the seats of government of other major powers, with particular attention paid to communication infrastructure and power plants. That's at least 99% of the Earth's ability to fight back taken out along with, if you're careful, about 10% of the population.
Quickly moving in with ground forces, you secure Chinese engineers, doctors (since many of your new hosts will be from poor regions, they're going to have debilitating but treatable diseases, and you're going to want to have access to good information on human medicine), and industrial infrastructure (this is likely the most costly part, but hopefully you were able to cripple the Chinese military and leadership in the initial attack). With China secure and the (largely unarmed and disproportionately adult) rural population being infested, you start building Kandrona pools. Unlike in the US in the books, you can do this openly - no one else has the technical ability to see what you're doing or the military ability to do anything about it - so you can probably get more built faster. After that, all you need to do is temporarily establish control of isolated regions of the world so that you can infest the people living there. This isn't difficult. Consider that the US military was able to (temporarily) pacify Iraq almost overnight and with virtually zero losses. The yeerks have better technology and very few remaining countries would still have the wherewithal to mount any sort of organized defense. You're looking at a year, at most, before the majority of the pre-assault population of Earth is Controlled (remember that without satellites and the like, most people in the world won't even be aware of what's going on until the yeerk invasion is on top of them, though they will know that they've completely lost contact with the US and other countries). And, of course, most people who do know roughly what's going on will think that the world is under attack by Hork-Bajir and Taxxons, so any place that still resembles civilization might well be willing to take in some "refugees".
In short, the best bet seems to me to strike very hard at the very small percentage of people who can hurt you, except for one country which you take over intact after just a few surgical strikes and which you use as a base of operations in taking over the essentially third-world remainder of the planet. Various sneaky maneuvers with Controllers can be tried later, since even knowledge of an alien invasion isn't going to cause people to take precautions against brain slugs (in fact humans might be generally more trusting of other humans than they otherwise would be). This nets you lots of Controllers really quickly, which seems to be what's required.
