After what level I can start work on my awesome project ideas?

I don't know what kind of project do you want to make. Is it localhost or external server based. After lv20 you'll be making complex programs at the end of each level, but don't worry - it's all well explained and you just follow the instructions making new classes and methods according to the objectives. But still it's just on your computer. After lv30 I am expecting to start with Internet apps. In theory you can start making something on your own after lv10 but this can teach you wrong patterns. For example there are several topics about Threads presenting you how to make them:

Thread thread = new Thread...;
thread.start;

And couple levels after you learn this way is only for teaching, better practice is to use ThreadPoolExecutor class. There's more stuff like this so better stick to this course. After lv10 when more difficult stuff will come out, you may start your GitHub account and upload there your finished CodeGym tasks with clear labels (eg. task1001-ForEachLoop) so you will have something to present at the job interview.