It is important to have the proper tools at some point to continue your progress mastering skills such as lighting and post processing, but the essential skills of the photography are not dependent on the camera you use. The camera is a tool. And as tool is important, like in any other craft. But any craftsman is an skilled person whether he has the best tool or the simplest.

 

 The qualities of great photographers are that

1 - They have an idea or concept: a story behind them
2 - They are taken in the precise moment,
3 - They make an excellent use of the available light, and
4 - They have an amazing composition. 
 These skills are the foundation of the great photography and you can exercise them with pretty much any device you have. The camera you have will do fine.
Get to now the functions of your camera. Some of them will be very useful. But the main thing here is to know the rules of photography and practice them a lot. Look for resources online and Youtube tutorials. There are a lot and they are very good. Don't give up. Keep shooting. Keep shooting. And keep shooting.

So turning your question back to you. Do you want to become a good photographer despite the fact of not owning a DSLR?  YES YOU CAN DO IT!