In the header footer tab, you can adjust the space reserved for the header.You may need to also adjust the paragraph formatting of the last paragraph in your header to change the space after setting.
There are tried and true methods to set up letterhead in Word.
See
How can I get a different header/footer on the second page? and
Setting Up Letter Templates - by Suzanne Barnhill, MVP
Here is a tutorial with sample documents demonstrating the concepts.
Letterhead Textboxes and Styles Tutorial
The key is to put your letterhead elements into the
First Page Header (and potentially into continuation Headers). This is true even if they are in places on the page outside of the traditional header area. This can be used to mimic different margins and insert logos.
The headers and footers are normally not the area of focus when writing letters and can be protected.