If you want to have no white margins at all, you will first need to go into the Print Setup and select "borderless" printing mode. Some printers offer a choice of borderless modes, but typically the image is silently enlarged a further few % within the printer, compared with how it is seen in the software application, to make sure that it "prints" across all edges. So you will lose a little of the image content that you see close to the paper edge in LR.
Once you have full borderless use of your A4 page back in LR, you will need to reduce LR's own page-layout "Margins" down to 0 on all sides.
This should allow your "Image Cell" to be enlarged so as to touch all the paper edges... even though the image itself may not, as yet, do so (because it is likely to be a different shape - aspect - than the A4 paper is).
You can alter the image's aspect ratio (crop) to match the A4 and fill it exactly, but you don't have to. Instead, you can select "Zoom to Fill" in the Image Settings panel. This enlarges your image until it leaves no white space in its cell - in effect, auto-crops dynamically to whatever shape that is. You can then slide the image "behind" this virtual window-frame, into the preferred composition.
In a 'picture package' or 'custom package' layout, you will need to hold Ctrl [Command] key down for doing this.