The best way one can install Dota 2 without downloading is to simply copy it from any friend of yours who has it on his/her personal computer (PC). This can be done by trying to download the Dota 2 from the internet, allow the download process to run for about 10 seconds or thereabouts, then pause it thereafter. The main reason for trying to download this is to set up the folder structure.
After this, we need to delete the local content from the Steam library. Right click on Dota 2 in the Steam library, you would see the option to delete the Local content, just click on that and it should delete.Next is to paste the copied Dota2 into the Steam app under common. Now reinitiate the installation of the Dota 2 again. It should immediately verify the existence of the game content.
There might be added contents that need to be downloaded that could require a few gigs of data, but you can just go to “Library” in the app, then select Dota 2, uncheck the DLCs that you do not need. With this, you would be left with just a few megabyte of download left.