Do NOT insert section breaks for this! This will incredibly complicate your document.

Do use the page break before setting for H1. Set the style for following paragraph to be H2 which does not have page break before.

Set up a second level 2 heading, say H2a, which does have page-break-before set. If you want, set a keyboard shortcut for that. The default keyboard shortcut for H2 is Ctrl+Alt+2. Since the only time you would be using H2 is when it follows H1, you could use that keyboard shortcut for H2A.

Understanding Styles in Microsoft Word
Why use Microsoft Word’s built-in heading styles? by Shauna Kelly