is it possible to stream this game with this hardware or do I need to upgrade
Yes. You would want to use the encoder on the integrated graphics or graphics card to handle the streaming workload in OBS or NVidias Shadowplay.
If you already have the system together, you may as well try and see how it fits your performance demands.
https://pcpartpicker.com/user/ChuyBeRaw/saved/Q6vcf7 this is my set up already I try streaming but I get frame drops alot
Do you play on 1080p or 1440p, if 1440p try streaming on 1080p, if you still get frame drops on 1080p lower the graphic settings from ultra down to high and just keep downgrading until you get the desired frame rate. Also that pcpp link has a 9900k and a 2080 so why did you put in the tittle that you have a 7700k and a 1060, just wondering.
sorry I overwrote the other this list instead of the other one
and I play on 1080p
I fixed my list now