Am I supposed to show up to new unit with unit patch?

You wouldn't be expected to report to your unit with a patch on. But, if you know for certain what unit you are going to, and know what patch they wear, no reason why you can't show up with it already on.

It might look good for you to show up with one on your uniform.

Recommend spending the 8 dollars on a unit patch. Don't be "that guy" wearing nothing or the "US Army" patch, might as well just scream "I'm new, look at me NCOs and find a reason to spend time with me"
When I first joined and arrived at good ole 3BCT 101 ABN, us new PVTs had the issued black belt (w/ BDUs), first set of pushups an NCO quickly grabbed it and yanked "teaching" us why it is a failure and why we needed a rigger belt.
Do your best to be squared away, you won't be perfect, but effort is noticed and carries a lot of weight.
WELCOME!!!

Great question. If you know where you are going and are financially able, do it. You show up and subconsciously show "co-ownership" in your new organization and overtly show everyone that you are ready to play on tha team. It is also a level of attention to detail that will seperate you from your peers. Good Luck

Just buy one, and if you can wear it, good. If you can't yet, put it in your pocket. Its a lot easier now than it was when you used to have to sew them on. I showed up to Drum with the 10th Mountain patch on and nobody said anything, but this was 2003.

Lots of good answers below and I will add the time and money you put into your career will be noticed. A good deal of people wait and expect the Army to provide everything and while we are really responsible, the best person to take care of you is you.

I have and havent it depends on how high speed you are and willing to show your pride in the unit. To put it simply, the more you are self reliant but also a team member, the better you look!

Back in my day, the Supply Sergeant gave me patches to sew on my fatigues and Class As and the wool fatigues that were obtained from CIF, if not already on them.

Wait until you in process. Good chance you’ll be issued patches. Save the money out of your pocket.

You are supposed to buy it from the PX when you first arrive to your duty station.

I would just verify the unit patch and have it ready. Or pop into supply and they’ll issue you a few. Not a huge deal if you’re new

you wait till they give it to you

Put it on! You’re in the big army now

It depends on your unit honestly, my first unit reamed me for it but my last unit couldn’t of cared less. Given I was the first soldier for my last unit so my CW3 (acting CO) wasn’t really paying attention to anything like that.