How to create automatically for every page footer in docx using C#

Question

I am creating a docx and I need a footer (for each page of a document) with timestamp and page (in this format: [present page] of [total pages]. Every post/code I've read online seems to indicate that I must create a footer manually for every page and write the page information manually: is it true? Is it not possible to write code in a way that, appended a footer to the main document, the docx automatically create itself every footer populating it with the right information?

Any advice?

[UPDATE] I am using DocumentFormat.OpenXml.Wordprocessing and, following Heinzi's example, I've created a new document, added a footer and than I analyzed the docx by Open XML SDK 2.5: footer is created by this method:

private void GeneratePartContent(FooterPart part)
    {
        Footer footer1 = new Footer(){ MCAttributes = new MarkupCompatibilityAttributes(){ Ignorable = "w14 w15 w16se w16cid w16 w16cex w16sdtdh wp14" }  };
        footer1.AddNamespaceDeclaration("wpc", "http://schemas.microsoft.com/office/word/2010/wordprocessingCanvas");
        footer1.AddNamespaceDeclaration("cx", "http://schemas.microsoft.com/office/drawing/2014/chartex");
        footer1.AddNamespaceDeclaration("cx1", "http://schemas.microsoft.com/office/drawing/2015/9/8/chartex");
        footer1.AddNamespaceDeclaration("cx2", "http://schemas.microsoft.com/office/drawing/2015/10/21/chartex");
        footer1.AddNamespaceDeclaration("cx3", "http://schemas.microsoft.com/office/drawing/2016/5/9/chartex");
        footer1.AddNamespaceDeclaration("cx4", "http://schemas.microsoft.com/office/drawing/2016/5/10/chartex");
        footer1.AddNamespaceDeclaration("cx5", "http://schemas.microsoft.com/office/drawing/2016/5/11/chartex");
        footer1.AddNamespaceDeclaration("cx6", "http://schemas.microsoft.com/office/drawing/2016/5/12/chartex");
        footer1.AddNamespaceDeclaration("cx7", "http://schemas.microsoft.com/office/drawing/2016/5/13/chartex");
        footer1.AddNamespaceDeclaration("cx8", "http://schemas.microsoft.com/office/drawing/2016/5/14/chartex");
        footer1.AddNamespaceDeclaration("mc", "http://schemas.openxmlformats.org/markup-compatibility/2006");
        footer1.AddNamespaceDeclaration("aink", "http://schemas.microsoft.com/office/drawing/2016/ink");
        footer1.AddNamespaceDeclaration("am3d", "http://schemas.microsoft.com/office/drawing/2017/model3d");
        footer1.AddNamespaceDeclaration("o", "urn:schemas-microsoft-com:office:office");
        footer1.AddNamespaceDeclaration("r", "http://schemas.openxmlformats.org/officeDocument/2006/relationships");
        footer1.AddNamespaceDeclaration("m", "http://schemas.openxmlformats.org/officeDocument/2006/math");
        footer1.AddNamespaceDeclaration("v", "urn:schemas-microsoft-com:vml");
        footer1.AddNamespaceDeclaration("wp14", "http://schemas.microsoft.com/office/word/2010/wordprocessingDrawing");
        footer1.AddNamespaceDeclaration("wp", "http://schemas.openxmlformats.org/drawingml/2006/wordprocessingDrawing");
        footer1.AddNamespaceDeclaration("w10", "urn:schemas-microsoft-com:office:word");
        footer1.AddNamespaceDeclaration("w", "http://schemas.openxmlformats.org/wordprocessingml/2006/main");
        footer1.AddNamespaceDeclaration("w14", "http://schemas.microsoft.com/office/word/2010/wordml");
        footer1.AddNamespaceDeclaration("w15", "http://schemas.microsoft.com/office/word/2012/wordml");
        footer1.AddNamespaceDeclaration("w16cex", "http://schemas.microsoft.com/office/word/2018/wordml/cex");
        footer1.AddNamespaceDeclaration("w16cid", "http://schemas.microsoft.com/office/word/2016/wordml/cid");
        footer1.AddNamespaceDeclaration("w16", "http://schemas.microsoft.com/office/word/2018/wordml");
        footer1.AddNamespaceDeclaration("w16sdtdh", "http://schemas.microsoft.com/office/word/2020/wordml/sdtdatahash");
        footer1.AddNamespaceDeclaration("w16se", "http://schemas.microsoft.com/office/word/2015/wordml/symex");
        footer1.AddNamespaceDeclaration("wpg", "http://schemas.microsoft.com/office/word/2010/wordprocessingGroup");
        footer1.AddNamespaceDeclaration("wpi", "http://schemas.microsoft.com/office/word/2010/wordprocessingInk");
        footer1.AddNamespaceDeclaration("wne", "http://schemas.microsoft.com/office/word/2006/wordml");
        footer1.AddNamespaceDeclaration("wps", "http://schemas.microsoft.com/office/word/2010/wordprocessingShape");

        Paragraph paragraph1 = new Paragraph(){ RsidParagraphAddition = "007C3796", RsidRunAdditionDefault = "007C3796", ParagraphId = "5404E3E7", TextId = "621D9DAC" };

        ParagraphProperties paragraphProperties1 = new ParagraphProperties();
        ParagraphStyleId paragraphStyleId1 = new ParagraphStyleId(){ Val = "Footer" };

        paragraphProperties1.Append(paragraphStyleId1);

        Run run1 = new Run();
        FieldChar fieldChar1 = new FieldChar(){ FieldCharType = FieldCharValues.Begin };

        run1.Append(fieldChar1);

        Run run2 = new Run();
        FieldCode fieldCode1 = new FieldCode(){ Space = SpaceProcessingModeValues.Preserve };
        fieldCode1.Text = " PAGE   \\* MERGEFORMAT ";

        run2.Append(fieldCode1);

        Run run3 = new Run();
        FieldChar fieldChar2 = new FieldChar(){ FieldCharType = FieldCharValues.Separate };

        run3.Append(fieldChar2);

        Run run4 = new Run();

        RunProperties runProperties1 = new RunProperties();
        NoProof noProof1 = new NoProof();

        runProperties1.Append(noProof1);
        Text text1 = new Text();
        text1.Text = "1";

        run4.Append(runProperties1);
        run4.Append(text1);

        Run run5 = new Run();
        FieldChar fieldChar3 = new FieldChar(){ FieldCharType = FieldCharValues.End };

        run5.Append(fieldChar3);

        paragraph1.Append(paragraphProperties1);
        paragraph1.Append(run1);
        paragraph1.Append(run2);
        paragraph1.Append(run3);
        paragraph1.Append(run4);
        paragraph1.Append(run5);

        footer1.Append(paragraph1);

        part.Footer = footer1;
    }

I copied this method and called

FooterPart footerPart1 = mainDocumentPart1.AddNewPart<FooterPart>("rId6");
        GenerateFooterPart1Content(footerPart1);

but I have no footer, any advice?