The mission "A New Dawn" is actually the first mission of the main campaign. It is fairly easy as the main objective is to declare independence from the crown. I will provide tips and tricks I have read in strategy guides when I was getting used to the game.
From the Main Menu select "New Game" followed by "Campaign" and finally "Changing the World"
Here the game will have you choose your Dynasty (Choose your pre-existing or create a new one). Upon choosing, a cut scene will begin. You can skip this with
For easiest completion, I recommend "Very Low" Economic AND Political difficulty, as well as "None" selected for disasters. I also recommend playing on "Cayo de Fortuna" as the landscape is easier to farm.
Once the game is loaded, you're pretty much on your own. Your mandate will be 4 years, but this can be extended by completing tasks. Blue tasks I consider secondary, while Red tasks are your main tasks that will progress you through the campaign.
The first missions are riddled with tasks. You do not need to complete them all, as they are meant to help get you used to the game.
I recommend having Cotton Plantations because early on they are the biggest producers. You should also look into Banana and Tabacoo Plantations, Logging Camps, Ranch (Pigs) and potentially a few Iron Mines. Having 2 Teamster and 2 Docks is plenty to keep up with Exporting. You can even take up a couple trade routes by scolling through the Docks menu.
When placing Plantations, Logging Camps and Ranches, try to situate them in the most effective area (Dark Green on the Grid. The spaces will be more Yellow if the soil is not sufficient).
Later on towards declaration you should have at least 4 Guard Towers and 3 Military Forts. This will ensure there is not much effort or loss while declaring independence.
Once you declare independence successfully, the Achievement pops