How to print first page of PDF from Second Paper Tray of multifunction printer using JavaScript button?

First of all you need to get the correct internal name of the printer in Acrobat.

To do that execute this code in the JS Console:

app.printerNames.join("\n");

It will output the names of the printers on your computer. Copy the name of the printer you want to use from that list and insert it into line #6 in the code below. Then execute that code to print the first page of the file to that printer, with the option to use the tray that matches the page size:

var pp = this.getPrintParams();
fv = pp.constants.flagValues;
pp.flags = pp.flags | fv.setPageSize;
pp.firstPage = 0;
pp.lastPage = 0;
pp.printerName = "<Printer name>";
this.print(pp);