It sounds like you want to avoid dragging something. But just for the record, there is a snapping option to center on the page.
I guess most people like to use key shortcuts. But also just for the record, these are the buttons in Align and Distribute dialog, to center something. Horizontal
Vertical
And as already mentioned, you have to choose Page from the Relative to: dropdown menu.
Or depending on your workflow, it might work to use Document Properties > Page tab > Page size > Custom size > Resize page to contents. So that if you have all the contents on your page placed relative to each other already, resizing the page to the contents can make it all centered as well. If I need something centered on the page, this is usually my solution. (And don't forget you can use the margins feature (of resize to contents) as well, to help, if needed.)