[b]Option A: Use hotstart.[/b]
Run a simulation without any runoff, just connect a constant inflow boundary condition to that basin. Run the simulation. Find the time step T when the basin has the desired water level. Use the result file as hotstart for your actual simulation, specifying time step T.
The advantage of the hotstart approach is that it mimics what you really want: including the remains of an event that happened before. The disadvantage of the hotstart approach is that you have to create a new hotstart file whenever you change the layout of your network.
[b]Option B: Dummy link[/b]
Before running a simulation, MIKE URBAN fills any node up the lowest connected pipe. This approach only works if in your current setup any connected pipe is higher than the desired water level.
Create a short link from your basin to a dummy node. Then set the upstream pipe level to the desired water level, see attachment (only visible when logged in!). The attributes of the dummy node don't really matter.
The dummy link isn't affected by changes in your network layout. On the other hand you have to bear with a typical model only element.