The thick jungle today most likely was not present in the past. Take, for instance, the site of Caracol. The Chases recently did a LiDAR survey of the region and found that it was heavily terraced, more terraced than they had originally thought and mapped over the last 20 years. If you went today you would find thick jungle only because no one lives at the site and uses the land/manages the landscape. Keep in mind that the landscape you see today is not how it always was in the past.

Arthur Demarest does a decent job describing the landscape of the Maya lowlands during the Classic Period.

To give you the five-minute version: The Maya agricultural system involved several different strategies, but one of the more common techniques was a sophisticated version of slash-and-burn agriculture. Essentially, the nutrients in most rain forests are in the vegetation, rather than the soil. So by cutting the plants down and burning the mass you would create a layer of nutrient rich ash that would serve as a basis for growing crops.

However, you'd only get a couple of seasons of fertile soil out of that before you have to abandon that plot of land. At that point, you have to let the field go "fallow" (wild) for years afterwards. You'd go farm somewhere else and let the rainforest reclaim that plot of land. Ten years or so later, you'd come back to that plot and start over. So ultimately, this means that the Maya landscape would have been a patchwork of wild areas and agricultural fields. Some plots would have been farmland, some would have been rainforest, and lots of the landscape was somewhere in between. These tracts of farmland interspersed with wild areas would also have been mixed with little hamlets and clusters of houses. It might be helpful to think of the areas around the edges of Maya cities as "suburban" rather than wild jungle.

In either case, it would have looked a lot more open than it looks today, and likely didn't impose that much of a barrier to the movement of troops. Especially considering that the Maya (unlike their counterparts in other regions of Mesoamerica) did not frequently engage in large scale warfare. The Maya did fight wars, but it was infused with ritual and political meaning and largely the domain of aristocrats. The large armies of tens of thousands of men fighting in tight formation is something we only really have direct evidence for in the Mexican highlands, where there are no rain forests. The Maya likely fought some battles of this nature, but the bulk of conflicts in the Maya Lowlands appear to have been smaller in scale and aimed at raiding enemy city-states for the purposes of taking captives.