When you create a network dataset using the Create Network Dataset tool, you can choose which type of elevation model you want to use: No elevation, Z-level fields, and 3D Z coordinates. If your data is 2D and does not have Z-level fields (FZLEV and TZLEV), then you would need to create the network using no elevation. This will still produce a valid and usable network dataset. You just may have some problems modeling overpasses and underpasses. You will want to carefully check those to make sure they don't have endpoints or vertices (depending on your connectivity policy) to prevent them from connecting at those locations (so the driver can't turn left off a bridge and start driving on the road that goes under it, for example). But as long as the roads don't meet at an endpoint/vertex at the location where they cross, it should still work just fine.
Here's some documentation that should help: https://pro.arcgis.com/en/pro-app/latest/help/analysis/networks/understanding-connectivity.htm
