The main difficulty is not the high guest count. You have four years and plenty of space for roller coasters. The problem are the trees and shrubs filling most of the space. Since removing them will cost money, you should plan carefully if you don't want to risk running out of money in the beginning. Start by building one small roller coaster, the Wooden Crazy Rodent Roller Coaster is a solid choice. Don't rely on pre-built designs. Instead, create your own. This way you are most likely to remove fewer trees. After that, build two gentle rides and a thrill ride, as well as some stalls. Set the park entry and/or ride admissions as you see fit.
Expand slowly, building more roller coasters and a few more flat rides whenever you can afford it. You will need a decent amount of roller coasters to get 1,600 guests, ten or more is recommended. Setting your research to only roller coasters every now and then is a good idea. As always, marketing can help you get some more guests if you are not meeting the requirement of 1,600 near the end.