Yes! You just need to customize a shortcut to do just that. When creating an Open Project Shortcut, you can select what specific project will be opened, or if Siri should ask each time which project needs opening. In the Add to Siri tab, click on Edit in Shortcuts and you will be redirected to the Apple Shortcuts app.
Expand the Open Project menu and in the Project Name field, either enter the name of the desired project to be opened, or select the Ask Each Time option if you want Siri to ask each time which project to open. Click on Done and then X to save your changes.