Is there any way to stop Steam downloading updates?

Answer would be - it depends. Some games require activation, and it might start downloading soon after the activation is over. Try starting Steam in offline mode and then launch the game - and see if it works

If you have the actual disc, or a Steam backup disc, then yes.

Once a Steam game is installed, you can go to your Steam library, right-click the game's name, choose Properties, click the Updates tab, and change the Automatic Updates dropdown to "Do not automatically update this game."

It's a good idea to go into Offline mode before doing this, or launching Steam while not connected to a network so that it doesn't start downloading the update automatically.

Important Note: Turning off auto-update is almost worthless on multiplayer games, as the servers tend to run the latest version. This includes such popular games as Counter-Strike (original and Source) and Team Fortress 2.

This method is a bit of a hack and not officially supported by Valve (i.e. it might break in the future). However, it has the advantage that you won't be able to accidentally trigger an unwanted update by playing the game while Steam is still running and online (but I would still recommend making a backup of the installation directory, just in case), and it has worked for at least the last 3 years, so Valve does not appear to be in any rush to fix it.

0. Find the app ID of your game. You can discover this number by going to the game's store page, right clicking anywhere, choosing "copy page URL," pasting it into Notepad (or any text editor), and extracting the number from the URL. For example, if you have the URL https://store.steampowered.com/app/1234567/Name_of_Game/, then 1234567 is the number we want.
1. Go to the game in your Library, and click (gear icon) > Manage... > Browse local files. This will open a file explorer window.
2. Go up two levels. You should see a bunch of files with names like appmanifest_1234567.acf, as well as some other files and folders.
3. Find the appmanifest file that corresponds to your game (has the same number we found earlier).
4. Right click the file, select "Properties", and check the read-only box, then click OK.
   On non-Windows platforms: Deny write permission, by whatever means your platform normally uses. On most Unix-like systems (macOS and Linux), the terminal command chmod a-w filename will remove all write permissions from filename. In most cases, chmod ug+w filename is the correct way to reverse this operation.
5. When you want to launch the game, you will have to run the exe directly, instead of clicking "play" in Steam. However, you don't have to quit Steam or put it into offline mode.
6. If you later change your mind and want to update, you will need to repeat this process, and uncheck the read-only box. Otherwise, Steam will refuse to update the game. This won't affect updates for any other games.

This has been tested extensively with Skyrim: Special Edition, and is confirmed to work for that game. I believe it should work for most games, but it is possible that it might fail to work if the game does something weird with its Steam integration (e.g. a game could manually check its version against whatever Steam says is the latest version, and refuse to run if it's outdated).

Try running the game with steam in "offline mode". I'm not sure what will happen if you switch to this if steam has already started downloading an update, but I think it's your best bet.

I'm only aware of two methods:

1. Close out of Steam and open the game's .exe manually. Its location can be found from Steam --> Right click game --> Properties --> Local Files --> Browse.
   Unfortunately some game exe's open Steam, so this method doesn't work for all games.

2. Start Steam in offline mode from Steam toolbar --> Steam --> Go Offline. Then it won't attempt to update before launching the game.

You can do it by opening Steam without internet then connect and then go online. However, if the game already started updating, you HAVE to let it finish or else steam won't let you play it.