Solo backpacking on trails in National Parks is not truly "solo". Most trails are quite popular and you will run into people a lot. Some parks require you to camp at established campgrounds, where there will be others. Not that great for those of us who like solitude, but really great for a beginner like you.

I find that to truly be solo, you almost have to go off trail. In this case you need many more skills- particularly navigation skills and micro-route finding. This may be a goal for you after you perfect solo backpacking in more popular places.

Going solo is more mental than anything else. It is all a matter of confidence and self-reliance, which are built by experience. At some point (and only you will know when that is) you will feel enough confidence to be really comfortable solo. Do not expect this at first, so do not get discouraged. Also, if you never adjust to it, do not feel defeated. Some people are just very social and do better and have more fun around other people. You will not know until you try it.

Remember, if you solo, be sure to leave a detailed travel plan with your family so if you go missing you have a chance of being found.