This can be achieved with Adobe Illustrator and CorelDRAW. If you don't have either then making this change would be tricky but not impossible in Acrobat Pro.
Rather than trying to add this background to your PDF directly, you would need to add your PDF to an premade PDF containing your background.
Let's presume you want page 1 of your document to have a blue background that fills your A4 portrait layout. I would create an A4 portrait page in Microsoft Word or PowerPoint and fill it with a blue rectangle or design. Then I woulkd create a PDF of this page and call it 'Background.pdf'
I would extract Page 1 of your original document and name it 'Page One.pdf'.
Then I would open 'Background.pdf'and import 'Page One.pdf' using the 'Import as Layer' option in the Layers Pane.
In theory your background will appear behind your original document.