Generating image with random String positions without overlapping in Java

i'm trying to randomly generate images that look similar to identity cards. I already generate different things like name, address and birth date but i don't want them to overlap.

I tried something like this:

public int[] getUnusedPos(int w, int h) {
    if(boxes.size()==0) {
        int x = rand.nextInt(screenWidth-w);
        int y = rand.nextInt(screenHeight-h)+h;
        return new int[] {x,y};
    }
    int x =0;
    int y = 0;
    boolean xFound = false;
    boolean yFound = false;
    while(!xFound||!yFound) {
        x = rand.nextInt(screenWidth+1-w);
        xFound=true;
        y = rand.nextInt(screenHeight-h)+h;
        yFound = true;
        for(Box b : boxes) {
            if(x>b.getX()-w&&x<b.getX()+b.getW()) {
                xFound = false;
            }   
            if(y>b.getY()+h&&y<b.getY()-b.getH()) {
                yFound = false;
            }
        }
    }
    return new int[] {x,y};
}

w and h are width and height of the box that should be drawn next. boxes is a list that contains the positions of all the drawn boxes before. I then randomly generate x and y coordinates and check if the new box would fit in the screen without overlapping with a different box.

For the first 2-3 boxes this works, but i need to draw 6 and it takes forever to find x and y values. I know there is a way to generate random ints in ranges, but i dont know how to define these ranges from the boxes i already drew.

Any ideas?