Studio gets install locally in the Program Files (x86) folder.
“C:\Program Files (x86)\UiPath\Studio”
Then, look for Studio.exe and run it.
I also suggest pinning the application to your taskbar, which then you can open your recent files by right clicking on it.
Once Studio is opened up, you can access your recent files also in the Open section:
Apologies if your version looks different.
Also, you can choose to save and move files around as you please, like if you want to save it on the Desktop or wherever.
Hopefully, this was your problem. If not, please provide more details and maybe I or someone can assist further.