Margin top after page break

I've got multiple h1s in a document (for sections of content) and they have margin-top: 1cm; (to space them away from the previous section content).
When there's not enough space at the bottom of the page they get moved to the new page which is as expected, but there's a blank space at the top of the page.

Is there a way to fix this so h1s have space above them where needed but they appear flush with the top of a new page?