Step 1: Understand SVG transparency
An SVG does not need a background. Empty areas remain transparent unless something paints behind the artwork.
That paint source is usually one of three things: a full-size rectangle or path, a fill on the root <svg> element, or a CSS background-color applied by the page or viewer around the SVG.
Before hunting for it, rule out the fourth possibility: nothing is painting at all and you are looking at the viewer. SVGSketch draws its own theme color behind your document and shows no checkerboard, so a file with nothing behind it still looks solid on the canvas. So does an image preview, a file manager thumbnail and most browsers on a blank page. Drop the file onto a colored page before you delete anything.
Step 2: Find the background shape
Open the Elements panel. Start at the bottom of the layer stack and look for a rectangle or path that covers the full viewBox, often a <rect> with x="0", y="0", and width and height set to 100% or to the viewBox dimensions. Select it and confirm that the highlight covers the whole canvas.
Step 3: Delete it, or set its fill to No Fill
If the shape only exists as a backdrop, delete it. If the file depends on that object for alignment, grouping, masks, or bounds, keep the object and stop it painting instead: open the Appearance panel and set the Fill Type to "No Fill", which writes fill="none". The panel spells out what that means - "No fill. Shape interior is transparent."
Step 4: Check the SVG element itself
If no full-size shape is selected but the SVG still appears to have a backdrop, check the root <svg> element itself: open the XML Inspector (F12) and look for a fill attribute or a background style on the root, and clear it there. If the SVG only looks white in a browser or image viewer, test it on a colored page before changing more artwork; the viewer may be supplying the white background.
Step 5: Export with transparency
For SVG export, transparency comes from the markup: if nothing paints a pixel, that pixel is transparent. There is no background setting on an SVG export because there is nothing to set.
For PNG, WebP and ICO, the Export panel offers a "Transparent background" checkbox and it is on by default - flattening is the lossy choice, so it is the one you have to ask for. The preview in the settings dialog switches to a checkerboard while it is checked, which is the fastest way to confirm what you are about to write. JPEG has no alpha channel at all, so the checkbox is absent for it and empty areas are flattened onto white.