Fullpage.js provides you a few methods (see them in action here)

Two of these methods will help you to move to specific sections or slides in your website:

• moveTo(section,slide) (codepen example) scrolls the page to the given section and slide
• silentMoveTo(section,slide) (codepen example) like the previous one, but it performs the scroll without animation

You can set one of this method to a button or use the fullpage.js callbacks to fire it when you desire.

In order to skip sections we can use the moveTo method in the onLeave callback. Here's a codepen.

And here's the relevant code:

new fullpage('#fullpage', {
    sectionsColor: ['yellow', 'green', 'purple', 'orange'],

    //events
    onLeave: function(origin, destination, direction) {
    	skipPages(origin, destination, direction)
    }
});


function skipPages(origin, destination, direction){
    if(destination.item.classList.contains('skip')){
        if(direction === 'down'){
            destinationIndex = destination.index + 2;
        }else{
            destinationIndex = destination.index;
        }
        console.log(destinationIndex);

        setTimeout(function(){
            fullpage_api.moveTo(destinationIndex);
        });
    }
}

In order to make it work for us we would have to add the class name skip on the sections that we want to skip. 

For example:

<div id="fullpage">
    <div class="section">Section 1 </div>
    <div class="section skip">Section 2 </div>
    <div class="section">Section 3 </div>
</div>

You might also find these articles relevant: