Can two people work on the same QGIS project in real time?

Brief answer: not in the way you describe ("like google doc").

First, it's important to realize that in "working" in QGIS, you are working with 2 types of files/documents.

There is the project, which contains information about what the layers are, how they are displayed, layouts, as well as all sorts of other settings.

Then, separately, there is the geospatial information for each layer. QGIS accesses that information, read or write, through an appropriate data provider.

There is nothing stopping you from running a copy of QGIS on different computers, each opening a copy of the project file. Then, any changes they make in the project file will be saved only in their own copy. You could, at your own risk, even try to have them access the same copy on some sort of shared drive, but whoever saves the project file last will win in terms of committing their version.

Most file formats for saving layers are also not multi-user friendly, at least in terms of read/write access. PostGIS is a notable exception, but outside the scope of this answer.

Therefore, with some exceptions, live multi-user work needs to ensure that users take turns making edits (as opposed to read only) to the project and to individual layers.

Editing to add: There is a plugin, https://plugins.qgis.org/plugins/gdrive_provider/, which attempts to get around some of these issues. I have not tried it.

Also see the Offline editing plugin (https://docs.qgis.org/3.10/en/docs/user_manual/plugins/core_plugins/plugins_offline_editing.html), which allows one or more users to work with a copy of their geospatial data in QGIS and then later synchronise their changes into a (master) PostGis database.