Is there a way to load images to user’s cache asynchronously?

You can preload images like this:

function preloadImages(srcs) {
    if (!preloadImages.cache) {
        preloadImages.cache = [];
    }
    var img;
    for (var i = 0; i < srcs.length; i++) {
        img = new Image();
        img.src = srcs[i];
        preloadImages.cache.push(img);
    }
}

// then to call it, you would use this
var imageSrcs = ["src1", "src2", "src3", "src4"];

preloadImages(imageSrcs);

Just fill in the URLs in the imageSrcs array and run this when your page first runs. The sooner you run it, the earlier your images will be available.

FYI, a related answer here: Image preloader javascript that supports events.