Is there a solution that I can play arma 3 on my laptop even though I don't have enough storage space without buying an external hard drive?
Cloud storage such as Mega
Clear the memory.
As @DerAllesHelfer said: move documents to a cloud and install the game.
First, you can free up a few GB. For this the https://www.netzwelt.de/...hnell.html
You can compress your operating system. Here to the https://www.turn-on.de/tech/ratgeber/windows-10-komprimieren-so-laesst-sich-speicherplatz-sparen-155721
You can move your data to a cloud, e.g. Store photos in Google Drive.
You can also compress data using a program such as http://7zip.org.
You can delete old savegames and keep in mind that you have to deactivate Steam Cloud, otherwise the data will be automatically uploaded again.
Delete a few unnecessary games / apps (is already on the first line)
But keep in mind that you delete data here that may also be missing. An additional HDD for games makes perfect sense. For a good deal with hard drives, keep the 20 euro per TB in mind. 4TB = 80 euro
Example HDD