The most reliable method is using the built-in Beta participation feature in the Steam client.
The earliest 2013 builds predate the "Arms Deal" update (August 2013), meaning there were no weapon skins or knives—just pure gameplay. Csgo 2013 Version Download
The year 2013 was a transformative period for CS:GO, marked by updates that defined the modern franchise: The most reliable method is using the built-in
If you want a specific build from later in 2013 (like the Arms Deal update that introduced skins), you can download "depots" directly from Valve's servers using the Steam Console. Csgo 2013 Version Download