Yes, I guess it’s kind of the point of SVGs to not have dimensions, but it has introduced a little bit of a complication that image tags didn’t have previously!
They can be exported from Illustrator with dimensions if the responsive box is unchecked in the SVG options modal (this is from file → export → export as):
(Another issue that I’ve run into that can be avoided in the export modal… If you’re embedding an SVG image directly on the page as markup it can also help to switch the styling to inline, otherwise styles from different SVGs can clash because they’ll likely use the same Illustrator class names)