Is it possible to programmatically modify or create a large number of graphic files at once?

I've used your question as learning opportunity. This script will replace the top page item of the active file with each Symbol in the file and export a PDF. I've included a file with 3 symbols for testing. You could add more. In reality you'd probably want to access the unique "animal" files from a folder.

• Copy the script and save as ".jsx" file in any text editor.
• Run script from "Other Scripts" menu:

swapSymbols();

function swapSymbols() {
    var aDoc = app.activeDocument;
    for (i = 0; i < aDoc.symbols.length; i++) {
        var oldSymbol = aDoc.pageItems[0];
        var newSymbol = aDoc.symbolItems.add(aDoc.symbols[i]).position = oldSymbol.position;
        var mySymbolName = aDoc.symbols[i].name;
        aDoc.symbolItems[0].translate(0, (-oldSymbol.height + aDoc.symbolItems[0].height));
        oldSymbol.remove();
        mySaveFileToPDF(mySymbolName);
    }
}

function mySaveFileToPDF(mySymbolName) {
    var aDoc = app.activeDocument;
    if (app.documents.length > 0) {
        var saveName = new File('~/Documents/' + mySymbolName + '.pdf');
        saveOpts = new PDFSaveOptions();
        saveOpts.pDFPreset = "[Illustrator Default]";
        PDFSaveOptions.generateThumbnails = true;
        PDFSaveOptions.acrobatLayers = false;
        aDoc.saveAs(saveName, saveOpts);
    }
}

Here is the sample file containing 3 Symbols:
dog.pdf