AoE3 download of game files (I have the serials from bought disks but not with me)

I’m currently in military service and sometimes have free time so my colleagues and I started to play AoE2 HD. I played AoE3 for several years and would really like to play it again right now.

I still have the vanilla, TWC and TAD disks at home but no access to them (and my laptop wouldn’t even have a drive to put it in) but someone could take a picture of the serials and send them to me. Do I have the ability to just download the game files anywhere?

I could buy it on steam but that’s wasted money since I already bought them. I would really love to play now :)