Use Windowed Borderless

Garry’s Mod by default can only use fullscreen or windowed. You can enable a windowed borderless mode which will allow Garry’s Mod to remain fullscreen but will also allow you to switch to other windows while it’s stuck loading.

Step 1: Open Garry's Mod Properties

Right-click Garry's Mod in your Steam library and click  Properties... .

Step 2: Add Launch Options

On the General tab, enter -windowed -noborder in the launch options text box at the bottom of the window.

That's it! Now when Garry's Mod is in the middle of loading, you can tab into other windows without issue!