You’d make me curse my monitor decision except it’s issued by work, so am stuck with it!
I have no idea why your employer is buying consumer hardware instead of the stuff Dell aims at businesses, because all of the Dell monitors I’ve ever seen at work (hundreds over the years in a couple dozen models) have had those mounting points.
Wall mounting was never an issue before, as I had a mahoosive desk (and, presumably, it was a cost-based decision). Of course now I’m working from home like the rest of mankind and trying to make my work kit fit into my teeny guest bedroom!
Your office IT department may have other monitors that do have the VESA mounting points. Perhaps they can swap out for a different monitor? Or even special order a business-class monitor for you. They’re really inexpensive, especially with corporate discounts. The monitor we usually buy costs us $108, while the list price is $230 and it’s on sale now for $180.
Not going to fly, unfortunately, am stuck with what I have. Don’t get me wrong, it’s actually a great monitor, just need to hang it up.
Well the OP doesn’t have to find the wall studs. 
Get a package of Red Head Masonry/concrete anchors. I’d suggest the linked anchors that are 2 3/4 long. The bit is included. It’s a small diameter Tapcon and won’t make noticable damage in the brick. The holes can be filled later with latex wall putty. Color it with brick dust.
You’ll have to make a larger hole in the 4x4 cleat. Your counter sinking deep into that 4x4. A 5/16:bit will work. Leave about an inch of wood for the Tapcon and use a washer under the hex head. I’d use 2 on each end of the cleat. A six inch long cleat will work well.
Use a hex driver to twist in the tapcons. The drilled pilot hole let’s them go in easily.
Lowes carries these too.
One tip. Check the package closely. People occasionally steal the bit out of the package. 
You may have to look at several packs to find one with the free bit.
Counter sinking isn’t difficult.
Use a 5/16 or 3/8 bit. Use tape on the bit to indicate when your 2 3/4 inches deep. That’ll leave roughly an inch of wood.
Use the tap con to mark the center of the hole. I think a 1/8 bit will let the tap con go through. You don’t want to damage the threads by forcing it through the wood. Insert the tap con with a washer.
You should have about 1 1/2 to 1 3/4" of the tap con sticking out the back of the cleat. That’ll give a secure connection to the brick.
I hope this isn’t to detaled. I get DIY questions from younger family members. I’ve learned replying with detailed email works out better.