The work will not come to you simply by itself. It is a misconception of the how the real world is.
I am afraid you need to "fight" to get involved on projects. Having a job offer is just an entry ticket to the game, it is not the game itself and does not warrant that you are going to be in the game.
-You need to do small steps, take simple tasks - get them done properly and make sure it is noticed.
-Networking; you should run to get to know the others and not the other way around, you need an agenda and a plan;
How big is your organization ? get appointment with managers and introduce yourself, one by one. Ask about the forecast, their workload, etc. Take notes. Dont hesitate to break the rules: if you can take an assignment out of the normal flowchart, let this be subcontracted to you. Worse case your managment will get the message and to keep you calm, they will try and keep you sort of busy
-Do not compare to other peers to make your self assessment - there is too much cognitive distorsion in that.
-You need to prove yourself competent to make sure people will asign you new projects, the manager can push one or two times but thats it. The rest is a matter of your reputation and attitude.
-Monitor your progress against your objectives, in this case the small tasks that have been handled. How many, what impact, etc
-Do not understimate assisting others engineers on stupid things: small doors open on big rooms.
Do all of the above and do it very fast, if not your mood will start to suffer as time goes by and then it can be a vicious circle. the problem will not solve by itself. Bottom line, as someone said someone is looking at how the hours are used. At some point you may get in trouble without this being your fault, is n it ? well not ... surviving is part of the equation.
Sometimes it comes easily. Sometimes not. But if you come over it, on the long run you it will play in your advantadge.
If despite all your efforts, nothing happens within a certain time frame - say 6 months from now - change company.
"If you want to acquire a knowledge or skill, read a book and practice the skill".