How to move entire session to the right?

No, there isn't a ripple push! Fortunately you don't need one. In your session, select the 'move' tool and hit Ctrl+A. This will select everything in your session, and just clicking on any of the highlighted files will give you the option to drag them either way. Or even onto some different tracks, if you want. The only thing you have to make sure of first is that none of the tracks are locked in time. If you feel more comfortable, you can group all the clips first, but generally there's no need to do that.

The other option, if you know exactly how much time you want to add at the start, is to put the cursor there and use Edit>Insert>Silence. This will bring up a box where you can enter the amount of time you want. Hit Okay, and the amount of time you selected will appear at the start - or anywhere else you put the cursor, in fact.