Hi,
Sure, it is possible. I recommend to check the magnifier and return button actions. You can basically set both of them to redirect to the WooCommerce results page.
In your case, I’m noticing see that the magnifier is not visible because of it’s white color. If it is not intentional, then you can change that here, so the users can see it, and engage. There is also a search text you can define with it here.
The documentation you are reffering to is for a search button within the filter drop-down/box, it is also usable, but I think in your case the magnifier with the text is probably better, since you are not using the filters.