If you have a letterhead, report or another type of document where you want the first page to have different headers and footers to the rest of the file, you can tick the Different First Page setting in the Header and Footer ribbon.
However, regular users will know this only means objects in the first page header and footer are not shown in the rest of the document (and vice versa). There isn't a setting that makes the first page margins different to the rest of the document.
Solution: Add a Table or Space After setting
Your first task is to determine which parts will have the smaller top margin - the first page or the rest of the document. You will then add a table or a Space After setting to the page(s) that should have the larger top margin.
If, for example, you want to make the top margin larger on the first page, you can either
insert a blank table in the header at 100% width and drag the bottom margin down, so it pushes the first page top margin down.
Enable the Show/Hide ¶ (keyboard shortcut: CTRL + SHIFT + 8 (Mac users: CMD + SHIFT + 8). Click inside the header area, go to the Layout menu and in the Paragraph group, increase the Space After setting by however many points you want, so it forces the top margin down.
If you choose the table option, it can be a 1-column, 1-row table - it doesn't have to have any more than that unless that's what you need. All you need to do is remember to turn the borders off, if your Word's default table format is a plain grid with black borders.
If you already have a table in your first page header, you can do the following, after select the table:
Go to the Table Layout ribbon and click on Properties
In Text Wrapping (in the Table tab), select Around. The Positioning button on the right becomes activated. Click on it.
Change the Bottom setting in the Distance from surrounding text section (in the middle of the dialog box). You can now push the top margin down using this setting.
Using the Space After option works for changing the Top margin. In the Footer, it makes sense to use Space Before to change the Bottom margin. For the left and right margins, it's best to use a table - insert one in the header and footer, position it on either the left or right side of the margin you want to change and drag the top or bottom borders to change the height, so the whole of the left or right margin is moved inwards.