There are a lot of factors that play into your future success. You have control over some of them, and there are others that are beyond your control. For now, focus on those you can control. As a new graduate, focus on building your skills and knowledge. New graduates all start at the same point - virtually none of them are of much value to the company. They hired you with the expectation that you will become valuable. If you want to be successful, focus on building knowledge as fast as you can. That is, make yourself valuable as fast as you can. You have complete control over your attitude and your desire to learn from each task (experience). You don't have complete control over which tasks you are assigned, but in many cases you can influence that. For example, pursue opportunities to get assigned to large projects. Large capital projects expose you to a maximum number of learning opportunities in a minimum amount of time. You'll get to learn from the specific tasks that you are assigned (they'll be low-level tasks at first) but you'll also get the opportunity to learn from what others on the team are doing. Pay attention during team meetings and soak up everything you can. That's especially true when they're trying to solve problems.
There are no companies that are true meritocracies. You'll see undeserving people advance faster than you - that happens everywhere. But in the long run, success largely depends on your knowledge and skills. Maximize the value of each experience. While you're completing a task, truly understanding how the process works and how the equipment works. For example, when you're doing simulations, notice the sensitivities when you make changes to streams or units blocks. You'll notice some surprising and interesting things. File that info (knowledge) away. Do the same when you're designing, say, a heat exchanger. Change the velocity of the streams, for example, and notice how the heat transfer rate changes. Understand why these changes happen. Over time, all that accrued experience will make you a valuable (knowledgeable) dude - valuable your company and valuable in the marketplace if you want (or need) to go elsewhere.
Some engineers let their experiences wash over them without benefiting from them. Others just want cook-book recipes for doing each task, without actively engaging their brain. Even those engineers can usually find jobs, but they won't have many opportunities open up for them - their destiny in mostly in other peoples hands rather than their own.