Can my rig support a 3060 or 3060ti?

[LitlClutch]

Budget (including currency): 

Country: Canada ( Ontario )

Games, programs or workloads that it will be used for: I Use it to game & stream and some light video editing & Voice Over recording.

Other details I really like small form factor PCs and ended up bying a MSI Nightblade X2B-249C. I think it has a 350w PSU... but not 100% sure since when I google the manuals that come up are never exact matches to my version of the Nightblade. They either say different CPU or RAM sometimes show a 1070 instead of the 1060 6GB i know my machine has. I think the 1070 variant might have a more powerful PSU, 400w or 450w PSU. Anyway what I'm curious about is weather or not my computer could handle a GPU upgrade to a 3060. it seems like its still fairly light on the power consumption. From what I've seen my 1060 6GB idles at 9w & max load of 121w and the 3060 is 17w with max of like 180w.
While I want to build a new unit starting with a video upgrade would allow me more time to save for the system while enjoying better performance then what I get... the 3060 is WAY more powerful then the 1060 6gb. Thanks for any help you might be able to offer.

CPU: Intel(R) Core(TM) i7-6700 CPU @ 3.40GHz   3.41 GHz
GPU: 1060 6GB
RAM: 16Gb

PSU: 350w?.. I think
 

[Queen Chrysalis]

You'll probably need a new PSU but yeah the rest is fine.  Go for a card with a smaller cooler though, the big honkers won't fit in there.  Check the PSU for sure though.

[Lord Szechenyi]

The PC will be able to handle the GPU, even at 350W

 

But if your PSU is a no name brand, I have no idea how efficient it is.

 

Better get (at least) a 400W psu...

[LitlClutch]

Smaller cooler & better PSU... ok. Thanks for the prompt responses. I wasn't sure if it would even fit.